Reigning champions Leicester hit the top of the table for the first time this season as they secured their fourth league victory in a row at Exeter.
A record attendance for Sandy Park – 10,495 – watched the game on a cold, clear Devon evening after the capacity of 10,700 had been reduced owing to the presence of the TV cameras.
Leicester had a dream start after less than three minutes after an error from wing Mark Foster as centre Manu Tuilagi collected the ball to set up a break before offloading to his brother Alesana to score.
Fly-half Jeremy Staunton was off target with his conversion attempt from out on the left but Exeter were quickly on the scoreboard with fly-half Ryan Davis landed a penalty to take him past 100 points for the season.
Staunton took Tigers further ahead with a 15-metre penalty from in front of the posts but then the Chiefs hit back as Davis split the posts again.
Midway through the half Exeter were given a penalty after wasting a good chance close to the Leicester line, but Davis was unable to land it.
With 10 minutes of the half remaining, Leicester demonstrated their experience, turning down a shot at goal and running, with Jordan Crane nipping in to score under the posts, with Staunton converting.
Exeter hit back before the break, though, with Davis kicking a 15-metre penalty.
Leicester started the second half strongly forcing Exeter to put in some big tackles to defend their line and, after applying the pressure for over five minutes, the Tigers resorted to a 40-metre drop goal attempt from skipper Geordan Murphy which was short and wide.
Exeter came back into the game and forced Leicester to concede another penalty and Davis drilled the ball between the upright from out on the left to reduce the arrears to three points.
As the game went in to the final quarter, England fly-half Toby Flood, who started the game on the bench after overcoming an adductor injury, missed a long-range penalty attempt minutes after coming on.
Exeter sensed a chance and full-back Luke Arcsott hacked in to the Leicester 22 where Flood failed to collect cleanly. Leicester were penalised in the subsequent play but Davis was unable to kick the three points.
Leicester then exploited a pick and drive to test the Exeter defence and Crane again found a gap for the Tigers third try with Flood adding the extras give the visitors a 10-point advantage.
With seven minutes remaining, Exeter sub Gareth Steenson kicked a penalty but then failed with another as Leicester clung on.