The home side out-scored Quins five tries to three with two touchdowns from Jason Shoemark plus one each from Brett Sturgess, Ben White and Sireli Naqelevuki with Gareth Steenson adding four conversions and three penalties.
The visitors replied with tries from Nick Evans, Ugo Monye and Karl Dickson while Evans added a conversion and two penalties with his replacement Rory Clegg landing a conversion and a penalty.
It was a welcome win for the Chiefs and Baxter will adopt a similar approach against reigning Heineken Cup champions Leincster next weekend.
"We will approach Leinster in a similar manner as we did Harlequins,' said Exeter head coach Rob Baxter. "We are a good side when we play. I want the players to go there and enjoy the experience the full 80 minutes.
"This was a fantastic game of rugby and, it's easy to say when you are on the winning end, it would have been a great game whichever way the last 10 or 15 minutes had gone. There were two sides really trying to play rugby.
"When you try to play rugby tries get scored, you also make mistakes and a few errors, and some of those errors really hurt us. Perhaps when we gave up the interception try or three penalties on the bounce can really hurt.
"It gave the game a bit of a see-saw momentum but what pleases me the most is that we came through those changes of momentum and came through them stronger at the end. I am more pleased with the mental challenges that we came through than the physical ones.
"Our preference is to keep the ball and make teams defend against us. Let's face facts, when Harlequins had the ball they were dangerous and they scored tries so it is a pretty sound approach to not let them have the ball as much as you can."
That is the first block of Premiership matches out of the way and Chiefs have won their three games at Sandy Park but lost the same number on the road. But Baxter says that they are slightly above the target on the basis of the fixtures they had.
He added: "We thought between 12 and 15 points would be a good return and would indicate a good solid start to the season.
"Now I would like to think that we can really attack the season in the way we did in this game. I don't think many teams will want to stand in front of us if we play like we did against Harlequins."
Harlequins' director of rugby, Conor O'Shea, accepted that his side didn't deserve even a loosing bonus but he full expects a reaction when they host Biarritz at the Twickenham Stoop in the Heineken Cup.
"We were rubbish, we were really poor," said O'Shea. "All the credit goes to Exeter for the way they played and we probably should have been beaten by a lot more. It's not terminal, far from it, as we have 20 points after six games.
"You don't mind coming and losing here because it is a tough place to come at the best of times. But we just got beaten up at the contact area, we lost all the collisions from minute one and it was a miracle that we were in the game for as long as we were.
"Credit goes to Exeter and we will learn a massive lesson in terms of what our desire needs to be if we are going to be up there where we want to be and will be at the end of the season.
"So this will be taken on the chin and the reaction will start next week. I don't care about results, and I said it at half time, I care about performance and today our levels of performance were not right."
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