Abbi Grant stroked City into the lead with a cool finish inside the post just before half-time.
Republic of Ireland international Noelle Murray knocked in a second.
It could have been more as City dominated - hitting the woodwork four times - and the three points ensure they remain two behind leaders Hibs.
Hibernian, who have played a game more, showed their title credentials with a thumping 8-0 win over Aberdeen.
Spartans came from behind to beat Rangers 3-1, while in SWPL 2 Forfar Farmington suffered their first defeat of the season against second-placed Motherwell, who cut the gap at the top to six points.
The season now pauses until August with Scotland coach Anna Signeul naming her squad for Euro 2017 on Tuesday.
At the start of the season it had been billed as a three-way title race between 10-in-a-row champions Glasgow City, the ever-improving Hibs and a Celtic side that had been busy in the transfer market.
However, now 13 points adrift of top spot and 11 off a coveted Champions League place, Celtic appear resigned to watching from the sidelines as Scotland's top two again battle it out for the league crown.
City had dropped only two points all season, a 1-1 draw with Celtic in March.
But just three months on Scott Booth's champions are again the form team and even Hibs will have their work cut out stopping them.
Nicola Docherty's curling shot was tipped wide then Hayley Lauder saw an effort palmed off the bar as City went on the front foot right from the start.
However, Celtic gave as good as they got in the early stages with Heather Richards cutting in from the left and testing goalkeeper Lee Alexander with an effort.
Grant shot over in 41 minutes, but shortly afterwards she broke the deadlock when she was unmarked inside the box and picked her spot.
Lauder could have done better with a weak shot from the edge of the box and only a great challenge from Sarah Crilly denied Grant again, while Sam Kerr's shot was tipped wide.
City struck the woodwork again when Lauder's shot hit the bar, but this time Murray was quickest to react and knocked the loose ball over the line.
Grant then hit the post before Murray shot over as the game became a procession for the visitors.
The opening goal scorer would be denied by the post a second time in the final 10 minutes before Natalie Ross hit the bar in Celtic's best chance of the game.
Celtic head coach David Haley: "It was a tough day at the office. Credit to City I thought they were really good today, they were at it right from the off, right from the first whistle. We found it difficult to deal with them.
"It's been an up and down season. We've dropped silly points away to Spartans and Rangers, games that with all due respect we should be winning. We've had some real highs and some really disappointing lows.
"We need to try and see what we can get out of the rest of the season. We've got a Scottish Cup to play for and make sure we finish closer to Hibs and City than we did last season. But to do that we have to beat them at one stage and hopefully we can do that in the second half of the season."
Glasgow City head coach Scott Booth: "We've been building up for the last six-to-eight weeks a really good level of consistency. The players have worked really hard on all the different areas of the park. It's difficult for the opposition when we press as hard as we press when we've not got the ball.
"We've managed to give really good game-time to all the players and that's really helped and we've become more fluid, tight as a unit, hard to beat and hard for teams to create chances against. It is a pity that we now have to break up for two months.
"We've done really good things in the first part of the season. To be in the position we're in having only drawn one game and lost one in the cup we've done really well."
SWPL 1
Celtic 0-2 Glasgow City
Hibernian 8-0 Aberdeen
Rangers 1-3 Spartans
SWPL 2
Buchan 0-2 Hearts
East Fife 2-3 Jeanfield Swifts
Glasgow Girls 0-0 Edinburgh University Hutchison Vale
Motherwell 3-2 Forfar Farmington
Glasgow City all but ended Celtic's Scottish Women's Premier League title hopes with a 2-0 win at the K Park in East Kilbride.