Nick Evans scored 14 points for the home team in what was their toughest test of the season to date.
Despite retaining possession from the kick-off, Exeter were caught not releasing just inside their half and Nick Evans opened the scoring with a third-minute penalty.
Less than two minutes after opening the scoring, referee Sean Davey awarded another penalty for Harlequins, this time for hands in a ruck, but Evans chose to kick deep into touch. The lineout led to a series of Quins attacking scrums, but Exeter stood firm.
And they should have scored a try on eight minutes when Matt Jess attacked up the left. He only had to pass outside to Luke Arscott who had an unopposed path to the line, but Jess tried to step inside and Chris Robshaw's flying tackle ended the danger.
Exeter's rucking turned Quins over for a second time, sparking a succession of phases that brought the best from the home defence.
Then Mike Brown grounded a Ignacio Mieres kick-ahead just over his goal-line, condemning the crowd to another tedious scrum comprising repeated re-sets.
Finally, John Andress was penalised for not binding, letting the hosts off the hook again in an opening quarter that belonged to Exeter in terms of possession and territory if not points.
Even when presented with a penalty on 22 minutes, Exeter fly-half Mieres fired wide of the far post.
Harlequins looked like a team who believed their seventh consecutive Premiership victory was somehow a matter of when not if, an attitude that was gradually dispelled by Exeter's attacking aspirations and some direct talking from the sidelines.
Even so, when Evans rifled home a second goal on 27 minutes, the scoreline was harsh on the visitors.
But Quins then made life even more difficult for themselves. Having been awarded a penalty, Davey reversed it after consulting assistant Paul Dix who revealed an off-ball incident that led to a yellow card for lock George Robson, hardly an ideal way to celebrate his 100th appearance for Harlequins.
Exeter, however, failed to punish their hosts while down to 14 - then gifted Quins another score with a soft penalty at the breakdown, and Evans completed his hat-trick.
Exeter were powerful in the scrum, and gave Harlequins problems in almost every engagement.
So it was early in the second half when Davey penalised Quins for charging at the first scrum, awarding a free kick, then for standing up in the next, awarding a penalty.
This time Mieres made no mistake, putting his team on the scoreboard. And when the home scrum buckled again three minutes later, Mieres repeated the punishment.
But Quins were in serious trouble on 54 minutes. Jess was held up just short of the line, but Exeter recycled well and a lobbed pass wide right for Bryan Rennie to score in acres of space. Mieres converted.
This galvanised Harlequins who changed gear, ignited their crowd and regained the lead inside seven minutes.
First Evans kicked his fourth goal after Exeter were caught offside, then a surging attacking ended with Karl Dickson's off-load sending fullback Mike Brown crashing through the defence for a fine try, converted by Evans.
The scrums continued to cause serious problems for the home side who became trapped close to their line.
But Quins somehow held out - and the roar when the referee finally awarded them a scrum was arguably the loudest of the afternoon.
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