The 24-year-old has started three of Exeter's four games this season.
"He was fantastic, not just in his carrying and his danger in that area, but some of his high-ball stuff was absolutely top drawer," Baxter told BBC Radio Devon.
"He looks a big, strong, quick, hungry rugby player and those are some of the qualities we saw in him."
Woodburn is in his second season at Sandy Park after moving from Bath, where he failed to break into the side.
He was a regular in the Chiefs team which made the play-off final last season and reached the last eight in the Champions Cup, an improvement which Baxter puts down to the work he has done on the training field.
"He's thriving on real regular game time and lots of good input from Ali Hepher, who's doing a fantastic job with the backs," Baxter said.
"They look like they're thriving on the way we're trying to play and the speed we're moving the ball and the angles we're running."
Exeter head coach Rob Baxter says winger Olly Woodburn is thriving after his two-try haul against Bristol.