The Devon outfit at one point possessed a 38-point lead as they ran in six tries to secure a 44-29 victory at Sandy Park in Pool 2.
Chiefs found themselves down to 13 men at one stage in the second half which disappointed Baxter, but he could not hide his delight at the result.
"In the first half we played with real intent and the attitude that we took on to the pitch following last week was absolutely fantastic - not just to attack the game but also the physicality and strength of the carries," Baxter told reporters.
"Obviously the battle for us is to keep the quality for longer periods. When you go down to 13 men you put yourself under a bit of pressure and we got ourselves down to 13 pretty unnecessarily. That flipped the whole game."
Chiefs travel to Glasgow Warriors in the group on Sunday.