Greg Fisilau was the star of the show Exeter as he ran in the opening try and also played a key role in Stephen Varney's 72nd-minute touch down that sealed victory.
Outstanding wing Campbell Ridl also crossed but Exeter finished one try short of claiming the bonus point that would have sent them into 2026 as Prem leaders.
But just one defeat in their opening eight matches of the season represents a remarkable transformation by Rob Baxter's side, who finished last year bottom of the table and playing in front of thinned out crowds at Sandy Park.
Leicester would have climbed into the top four with victory but remain just outside the play-off places.