The Chiefs maintained their unbeaten home record by beating Quins 42-28 at Sandy Park.
Baxter hailed the Devon outfit as "exceptional" after watching his side run in five tries against last season's Premiership winners.
"That was a fantastic game of rugby," said Baxter. "You had two sides out there who were not only looking to play rugby, but who were going at each other hammer and tongs for 80 minutes. In the end we've come out on top and got what I think we deserved for our efforts, which is very pleasing.
"I thought the attitude of our players was fantastic. At times I kind of think we had to weather a few storms out there because it was end-to-end stuff and the momentum kept see-sawing between both sides. The crucial thing, however, was that we never let any of that affect us.
"We went points up, we went points behind, and we also gave away a soft interception and put ourselves under pressure. However, that almost galvanised us in some ways because we didn't let anything dent us. Nothing seemed to hurt us out there today and that's one of the most important qualities a team can have."
Chiefs take on holders Leinster in the Heineken Cup this Saturday.