Chiefs showed mental strength
Gareth Steenson was in fine form at Sandy Park as he racked up all 19 points on the way to victory after kicking things off with a try after five minutes.
Owen Williams turned over two penalties for the Tigers who looked dangerous at times but never found the killer touch.
And for Baxter that was all down to the character of his side who defended well and capitalised on Leicester's errors.
"We have always been able to score some points but there have been moments in the games where they have seized momentum from us and rammed it home.
"Today we have weathered those storms a lot better, even when it got raggedy we actually came through the messy bits a bit better than Leicester.
"That was backed up by our scrum which functioned today and our driving game functioned too and, defensively, to only concede six against Leicester is fantastic.
"Things went really well for us and when you play Leicester you have to overcome some mental battles as well as physical ones and today we came through a few.
"Gareth [Steenson] was fantastic and the scrum was too and I think the whole pack stood up really well and we dominated them in the area."
The hosts got off to a flying start with Steenson crossing after two mauls had got his side close to the line and then turning over the conversion.
A penalty on 37 minutes was to follow before Williams turned over the first points for the Tigers – though Steenson's kick after 42 minutes made it 13-3 at the break.
The visitors started well after the break and Williams pulled them within three on 62 minutes before Steenson restored the ten-point gap with six minutes left to play.
Riccardo Brugnara then saw yellow for the visitors before Steenson closed out the win – Leicester boss Richard Cockerill full of praise for the Chiefs.
"I think you have to give credit to Exeter because we were on the back foot for a lot of the game," he said.
"You win the physical battles and we couldn't get a foothold in the game properly and that cost us.
"They are a good side and if you don't play accurately enough, which we didn't, and you don't front up physically, which we didn't you are going to get punished.
"That's what happened today but its round four and there is a long way to go and we have a lot to get better at."
@premrugby
