After an uneventful first 40 minutes, Mawson took too much time on the ball in a dangerous area and Etienne Capoue, on his return from injury, nicked the ball off the young defender and fired home at the second time of asking.
Swans captain Gylfi Sigurdsson strolled through the Watford defence right at the death but gave Heurelho Gomes an easy save as his side fell to their sixth straight away defeat. Their only consolation is that relegation rivals Hull were well beaten at Stoke.
Swansea, now winless in six Premier League games, face a continued battle to survive, but Walter Mazzarri's Watford look to have earned another season of Premier League football.
Sigurdsson was once again the bright spark for Swansea and had their best chance of the first half, but his effort was turned away by Gomes at his left post.
Watford captain Troy Deeney, reinstated to the starting XI after he was dropped to the bench for their 4-0 loss to Tottenham, could have put his side ahead but his first-time shot was tipped over the bar by Swans keeper Lukasz Fabianski.
The game looked to be winding down to half-time when centre-back Mawson hesitated in a dangerous area and, as he turned to send the ball back to Fabianksi, Capoue stormed in.
The Watford midfielder's first shot was blocked by Swansea keeper Fabianksi, but his rebound found the target as Swansea looked stunned.
The second half offered very little, but Watford's defence, which has been leaky of late, looked far more assured with Sebastian Prodl back in the mix and they held on to take all three points.
Paul Clement took over from Bob Bradley as Swansea manager in January and saw an initial upturn in form after his appointment - he won three of his first four games in charge.
And his side were five points clear of the bottom three at the start of March.
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But a horror run of just one point from six games has seen them slide back into the relegation zone - a stalemate with Middlesbrough is all Clement's men have to show for their efforts in recent weeks.
Swansea have five games left to secure their top-flight survival and extend their six-year run in the Premier League.
It looks increasingly like it could be a straight shootout with Hull City, who sit just two points above them having lost 3-1 at Stoke on Saturday.
But of the two, Swansea look to have the trickier fixtures, with next week's home game against Stoke probably one they have to win.
Watford manager Walter Mazzarri's fears of a slide down the table towards the end of the season will have been eased by his side's third home win in a row.
And the three points, which keep Watford 10th in the the table, will also have delighted the club's somewhat over-zealous owners.
The Pozzo family completed a takeover of the club back in 2012 - and have sacked seven managers in their time in charge.
Wanting to improve on a disappointing end to the 2015-16 season, they let manager Quique Sanchez Flores go with the club in 13th place - and his predecessor's fate will surely be at the forefront of Mazzarri's mind.
The Italian has faced criticism this season over his grasp of the English language and coaching techniques.
But his side, who have been plagued by injuries in recent weeks, were buoyed by the return of Capoue and ground out a tough victory.
They can start preparing for life in the Premier League next season - a campaign Mazzarri plans on being a part of.
Former Chelsea and England midfielder Frank Lampard: "I understand if Paul Clement seemed downcast at full-time. It was disappointing from Swansea's perspective - the one thing you expect as a manager is effort and a desire to get out of the situation they are in. That was slightly lacking from the start today.
Swansea were short in their energy and what they put into the game. It's a confidence issue - they are on a bad run and gave sloppy balls away throughout the game.
"It looks like a straight fight now between Swansea and Hull for that last relegation position. I watched Hull today and they are a team creating chances. You can see that they have some momentum."
Watford manager Walter Mazzarri:
"We knew it was going to be a very tough game. We could have killed the game off but we didn't and we had to suffer until the end.
"It is normal that when a new manager comes, he has to give his identity to the team and it takes a bit of time. Now the squad are playing good football.
"Until the numbers say we are safe, we are not. I don't want my players to relax and I want to play with the same formation in order to get ready for next season."
Swansea boss Paul Clement:
"I think we did enough defensively. The goal has come for an individual error and Alfie [Mawson] knew that straight away. It's a big mistake.
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"Offensively we got the ball into some good areas but we were missing a clinical edge in the final third. That for me was the difference.
"We had over 45 minutes to try and get out of that situation but we couldn't get the breakthrough.
"Hull not winning today keeps things the same but for me it's a missed opportunity not to get a point today.
"The next one is a must-win game for us. It's the biggest game the club has had in years.
"We will probably need three wins out of the last five to stay up. And I'm not even sure that would be enough."
Swansea are at home to Stoke, while Watford host the Swans' relegation rivals Hull - both games are next Saturday and 15:00 BST kick-offs.
Match ends, Watford 1, Swansea City 0.
Second Half ends, Watford 1, Swansea City 0.
Attempt saved. Gylfi Sigurdsson (Swansea City) right footed shot from the centre of the box is saved in the centre of the goal.
Attempt missed. Gylfi Sigurdsson (Swansea City) header from the centre of the box is close, but misses to the left. Assisted by Borja Bastón with a cross.
Foul by Stefano Okaka (Watford).
Martin Olsson (Swansea City) wins a free kick in the defensive half.
Attempt saved. Abdoulaye Doucouré (Watford) right footed shot from outside the box is saved in the centre of the goal. Assisted by Valon Behrami.
Stefano Okaka (Watford) wins a free kick on the left wing.
Foul by Kyle Naughton (Swansea City).
Stefano Okaka (Watford) wins a free kick on the left wing.
Foul by Leroy Fer (Swansea City).
Substitution, Watford. Valon Behrami replaces Tom Cleverley.
Delay over. They are ready to continue.
Delay in match Daryl Janmaat (Watford) because of an injury.
Delay in match Borja Bastón (Swansea City) because of an injury.
Foul by Daryl Janmaat (Watford).
Martin Olsson (Swansea City) wins a free kick on the left wing.
Substitution, Swansea City. Jordan Ayew replaces Fernando Llorente.
Offside, Swansea City. Leroy Fer tries a through ball, but Fernando Llorente is caught offside.
Attempt missed. Etienne Capoue (Watford) right footed shot from outside the box is too high. Assisted by Stefano Okaka.
Offside, Watford. Daryl Janmaat tries a through ball, but Stefano Okaka is caught offside.
Substitution, Watford. Stefano Okaka replaces M'Baye Niang.
Offside, Watford. Abdoulaye Doucouré tries a through ball, but M'Baye Niang is caught offside.
Corner,  Watford. Conceded by Kyle Naughton.
Offside, Swansea City. Borja Bastón tries a through ball, but Leroy Fer is caught offside.
Foul by M'Baye Niang (Watford).
Kyle Naughton (Swansea City) wins a free kick in the defensive half.
Attempt missed. Fernando Llorente (Swansea City) header from very close range misses to the right. Assisted by Kyle Naughton with a cross.
Substitution, Swansea City. Tom Carroll replaces Jay Fulton.
Corner,  Watford. Conceded by Federico Fernández.
Substitution, Watford. Christian Kabasele replaces Nordin Amrabat.
Foul by Sebastian Prödl (Watford).
Fernando Llorente (Swansea City) wins a free kick in the attacking half.
Etienne Capoue (Watford) wins a free kick in the defensive half.
Foul by Martin Olsson (Swansea City).
Attempt blocked. Borja Bastón (Swansea City) right footed shot from the right side of the box is blocked. Assisted by Fernando Llorente.
Substitution, Swansea City. Borja Bastón replaces Luciano Narsingh.
Attempt missed. Etienne Capoue (Watford) header from the centre of the box is close, but misses to the right. Assisted by Abdoulaye Doucouré.
Attempt missed. Abdoulaye Doucouré (Watford) right footed shot from outside the box is close, but misses the top right corner.
Corner,  Watford. Conceded by Federico Fernández.
Swansea defender Alfie Mawson made a costly error as his side were beaten by Watford at Vicarage Road to remain two points adrift of Premier League safety.