Two tries in a seven-minute spell early in the second half kept Leinster's hopes of remaining in the Heineken Cup alive, but they were forced to battle hard to secure a 29-20 win against newcomers Exeter.
The reigning champions will have to wait until Sunday to see if they or Munster, who welcome Racing Metro, progress to the quarter-finals as one of the best second placed sides alongside Montpellier.
Gordon D'Arcy, Rob Kearney, Brian O'Driscoll and Jamie Heaslip scored the tries for Leinster.
Exeter went in to the break with a 17-12 lead after a penalty try plus a touchdown from Neil Clark with Gareth Steenson converting both and adding a late penalty. Leinster replied with tries from D'Arcy - converted by Johnny Sexton - and Kearney.
Leinster regained the lead early in the second half with a try from O'Driscoll, converted by Sexton - who then added the extras to the bonus point try which followed quickly through Ireland skipper Heaslip.
Steenson replied with a penalty which was cancelled out by Sexton before the Chiefs had Ben White sent to the sin bin in the closing minutes, while Leinster's Mike Ross was also yellow carded soon after.