A Dave Ewers try with five minutes remaining sealed a comeback victory for the European champions at Sandy Park on Saturday.
Chiefs had to overcome a 13-point deficient in the second half to claim a narrow win, but Quins pushed them all the way.
In a game that pitted second place Chiefs up against third place Quins it was the Londoners who got the first points on the board when Danny Care touched down after fine work from James Chisholm and Alex Dombrandt.
The Gallagher Premiership player of February Marcus Smith added the extras to give Quins a 7-0 early advantage on the day he made his 100th appearance in a Harlequins shirt.
Chiefs responding following an attacking line out with Stuart Townsend going over with Joe Simmonds converting it was all square. But a Smith penalty made sure the visitors went into the break with a slender 10-7 lead.
Exeter handling errors throughout the first half continued into the second with Quins picking up their second try of the afternoon with Scott Baldwin rumbling over. Another three points from the boot of Smith extended the visitors advantage to ten points.
Harlequins looked to have run in their third try of the afternoon when Ben Tapuai crossed following a Care grubber kick. Only for the tmo to rule out the scoring effort for a knock on from Dombrandt.
However, Quins were awarded a penalty with Smith knocking over another three points.
It was time now for Chiefs to prove why they are double champions after winning the Premiership and Champions Cup last season. Following a pick and go Harry Williams was driven over.
With 75 minutes on the clock Ewers powered over from short range. Simmonds converted to give Chiefs the lead for the first time in the match.
With 80 minutes up and the clock ion the red zone Quins pushed for the line. They came very close before Exeter won a crucial turnover to edge out Harlequins in the narrowest of margins with Quins returning back to London with a losing bonus point, when at one stage it looked like they would be coming back with four points.
Exeter Chiefs 21 Harlequins 20
Gallagher Premiership Saturday 13th March 2021
By Peter Moore