Neil Clark went over for the Chiefs on 16 minutes and they were level thanks to Gareth Steenson's conversion.
The next try took another 10 minutes and the visitors were again ahead, Rob Kearney going over, but Sexton this time went wide of the sticks.
Exeter were awarded a penalty try eight minutes from half time. Steenson kicked the conversion before putting over a penalty to put the hosts 17-12 up.
The second 40 minutes was a different proposition with Leinster getting themselves on top.
Steenson added a penalty with 10 to play but the Chiefs were unable to force another try.
A final penalty confirmed the 29-20 win.