Rob Baxter's side never got going and were forced to forfeit their eight-game winning streak as Nathan Earle crossed the line either side of the break to rock the boat at the top of the table.
Harlequins, who had lost their previous eight games against Exeter, impressed from the off as rapid-fire scores from James Chisholm and Earle handed the initiative to the hosts ahead of the European break.
The Chiefs arrived at The Stoop safe in the knowledge they had not lost away from home since mid-February, but they quickly realised they were in for a tough knock from the off when James Lang kicked an early penalty.
Chiefs soon rediscovered their table-topping form by immediately breaking back from a set-piece down the left flank as Matt Kvesic escaped from the rolling maul to crash over the line for the first try of the evening.
Despite Exeter seeing the lion's share of possession, it was Harlequins that engineered the next breakthrough on 28 minutes as captain Chisholm found his way through a minute gap to dive across the line and give the hosts an 8-5 lead.
Quins did not let up there though as they found an uncharacteristically wide section of space in the Chiefs defence to exploit and Earle did exactly that when the ball was switched to the left and he sprinted down the wing to score for a 13-5 lead at the break.
With Baxter's words ringing in his players ears, his side rediscovered their ruthless streak courtesy of a sloppy passage of play from Gabriel Itoye and Marchant.
As Exeter pressed home from the line-out, they received their due reward as the skipper Jack Yeandle went over the line from the rolling maul to reduce the deficit to a solitary point.
But Quins refused to wilt and instead drove their way up the pitch as a moment of magic from England's Mike Brown set Earle away to score his second try of the night. Lang added the extras.
True to Exeter's form they did not give in easily and replacement Ollie Devoto forced the Chiefs back to within a point once more from another set-piece try.
With the clock ticking down Quins did not panic and after a wonderful spell of possession they were rewarded with a penalty, which Marcus Smith fired between the posts.
Marchant's try put the icing on the cake in the final minutes before a consolation try from Ian Whitten and conversion from Gareth Steenson set up an intense final flurry – but to no avail as Quins held on for a superb win.