Gareth Steenson, starting in place of Ignacio Mieres, kicked an early penalty to give Exeter the lead.
Harlequins had a chance to strike back through Nick Evans, whose poor kicking cost Quins against Saracens last week, but Evans kicked his effort wide.
Evans was given a second penalty opportunity five minutes later, and this time took full advantage to level the scores.
Steenson and Evans again exchanged penalities before the Quins fly-half pounced on a Steenson kick to touch down and pull the score back to 13-11.
Exeter extended the lead with another penalty but, shortly before the beak, consistent Quins pressure allowed Ugo Monye to break through and give Quins an 18-16 half-time lead.
The Chiefs regained the lead early in the second half, with a pitch-length move sending Ben White over for a try.
Once again Exeter hit back, this time through Jason Shoemark, who scored two brilliant tries to give the Chiefs a 10-point lead at 35-25.
Rory Clegg put Harlequins within seven points with a late penalty but big Sireli Naqelevuki powered over late in the game to secure a memorable 42-28 victory for the Chiefs.