A late Luke Arscott try not only secured a first Aviva Premiership double over defending champions Harlequins but also keeps Exeter Chiefs in the hunt for a Heineken Cup spot.
A fine Ugo Monye in the first half proved the difference as the home side went into the interval narrowly ahead at 10-9.
The boot of Gareth Steenson had kept the visitors in the game in the first half but after the restart the Chiefs crossed twice, first through lock Damian Welch and then late on with Arscott for a first away win since downing London Irish in November.
In the reverse fixture Quins had been beaten 42-28 and hosted Exeter looking to avenge that defeat, in the midst of a fine run that had seem them lose just once in their previous 13 games.
And they looked like doing exactly that after six minutes as wing Monye scored a superb opening try for the home side. Jordan Turner-Hall had options on his left shoulder and by using fellow centre Matt Hopper as a dummy runner he timed his offload to Monye to perfection and he raced away, Nick Evans converting.
But Harlequins discipline let them down in the next ten minutes as first Nick Easter failed to roll away to give Steenson the simplest of penalties, and then they were offside to allow the chiefs fly-half to bring his side to within a point of their hosts.
Evans’ compatriot Ben Botica then joined him at the Stoop after 20 minutes as Olly Lindsay-Hague went off injured.
But Evans kept hold of the kicking duties but his next effort, a penalty out on the left, had the line but fell just short.
And on 29 minutes he was made to pay as George Robson was pinged for offside and Steenson kicked his third three-pointer to put Exeter into the lead for the first time.
Quins were enjoying plenty of possession but couldn’t break down the tight Exeter defence, the reigning champions having to settle for a penalty from Botica to go back in front.
Kiwi Botica then had another shot at the posts a minute before half-time to give Quins some breathing space but he missed, meaning the home side had to make to with a 10-9 interval lead.
And three minutes after the restart this see-sawing game swung back into the visitors favour as Steenson kicked his fourth penalty as Quins were pinged for not releasing.
However Botica atoned for his first-half miss and knocked over two penalties of his own to give Quins a four-point lead.
But back came the Chiefs and after Steenson added another penalty they grabbed their first try.
Fly-half Steenson was the architect, making a great break down the middle only to be tapped just before the line. However Exeter remained patient and the ball found its way to Welch who barged over.
Steenson added the conversion for a four-point lead and full-back Arscott made the game safe with seven minutes left, collecting a box kick before racing through to spark wild celebrations among the travelling contingent.