Baxter makes one change from the team that beat Saracens last weekend, with fit-again Olly Woodburn replacing James Short, but Wasps are without injured Australian star Kurtley Beale, so Willie le Roux moves to full-back and Josh Bassett features on the wing. Both clubs finished on 84 points, but it was Wasps who claimed pole position courtesy of their greater win ratio.
The Wallaby, 28, has not recovered from a hamstring injury picked up in their semi-final victory over Leicester.
Exeter chairman Tony Rowe said: "Coming here a year ago and losing I know the pain, but I'm very pleased today".
In what was an enthralling final, 80 minutes of rugby couldn't separate the sides as it was locked at 20-20 following the final whistle.
"To be standing here from where we were seven years ago is absolutely unbelievable".
Exeter led 14-10 at the end of a first half which it dominated after Jimmy Gopperth crossed on the stroke of the interval after scores from Jack Nowell and Phil Dollman for the Chiefs.
The Chiefs opted against a virtually guaranteed three points and instead went for the scrum, and did the same minutes later as the clock ticked down and it looked like poor decisions when Wasps forced a turnover.
Chiefs turned down one easy penalty chance but in a dramatic finish took the clash into extra-time when Steenson kicked a penalty with 30 seconds to go.
However, rugby fans everywhere enjoyed it for what it was, a thoroughly entertaining game of rugby between two top teams.
"I was hoping we would get the try so it wouldn't come down to me kicking a goal". Saracens were experienced last year and it was still a pretty tight game, so we have to make sure we don't expect that having that experience from last year will be that big a factor.
Wasps poked their noses in front for the first time three minutes into the second half as Hughes showed all his mighty strength and power to shrug off a posse of Chiefs rivals and spark a surge down field.
"I think Steeno was right, it did feel different after the game last week", said Baxter.