After Charlie Hodgson's early penalty put Sarries ahead, Marcus Watson scored two converted tries to put the visitors 14-3 up at half-time.
A brace of tries from Jackson Wray put the hosts back in front before Maro Itoje's score secured victory.
Newcastle secured their top-flight status for next season despite defeat, as London Irish lost to Harlequins.
The Falcons deserved their lead at the break, which came courtesy of Watson's fine finishing, first beating Chris Ashton in the corner and then getting on the end of Chris Willis' clever grubber kick.
However, Saracens' forward pack secured victory in the second-half, as their attacking line-out set the platform for a series of rolling mauls which allowed them to score their three tries.
Victory at Allianz Park provided the perfect send-off for Sarries flanker Jacques Burger who made his final professional appearance before retirement.
The champions will have to wait to find out their play-off semi-final opponents, with Leicester occupying fourth place heading into the final round of matches.
Saracens director of rugby Mark McCall:
"I think we weren't able to play the way we wanted to during the first half.
"Last week took a lot out of us and crucially we also didn't train a lot this week. A lot of the players went to Europe for two or three days and had a phenomenal time.
"I think we showed our experience in the second half to turn the situation around; that's the important thing.
"We were able to fall back on some good fundamentals that we've had for a long time."
Newcastle director of rugby Dean Richards:
"We had a torrid time in the autumn with 20-odd injuries and we didn't get a win until Christmas.
"Since then, it's been a lot better and that's the frustrating thing. Had we started it off with the form like in the second half of the season then we'd have been nowhere near the bottom.
"The boys are desperate to go out there and play well and string good performances together.
"We did it in one half today and second half we weren't quite so good, so next week hopefully we'll put together two halves."
Saracens: Ransom; Ashton, Bosch, Barritt (capt), Wyles; Hodgson, Wigglesworth; Barrington, Saunders, Lamositele, Itoje, Hamilton, Rhodes, Burger, Wray.
Replacements: Brits, M Vunipola, Figallo, Smith, Brown, Spencer, Mordt, Tompkins.
Newcastle Falcons: Hammersley; Tait, Harris, Powell, Watson; Willis, Young; Vickers, McGuigan, Vea, Botha, Robinson, Welch (capt), Temm, Wilson.
Replacements: Hawkins, Rogers, Foster, Green, Mayhew, Tipuna, Catterick, Penny.
Referee: Ian Tempest.
Saracens guaranteed top spot in the Premiership with a comeback win at home to Newcastle Falcons.