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.
Unbeaten Clermont Auvergne booked a home draw in the Heineken Cup quarter-finals with a bonus-point 29-0 victory as the Scarlets suffered their second competition whitewash in 17 years of European rugby at Parc y Scarlets.
Clermont captain Aurelien Rougerie registered the bonus-point try 14 minutes from time, adding to earlier scores from Napolioni Nalaga, Morgan Parra and Benson Stanley.
It was the Scarlets' seventh defeat in eight games in all competitions since the beginning of December.
The Scarlets were much better side in the second half but still failed to break their duck.
Glasgow put an end to Northampton's hopes of a Heineken Cup quarter-final berth as Peter Horne's last-gasp try secured a 27-10 victory at a frosty Scotstoun Stadium.
In a game that marked Soane Tonga'uiha's 200th appearance for the visitors, Gregor Townsend's players achieved the Warriors' first win in this season's tournament against their head coach's former club.
The match will be remembered for the wonderful final-minute try from Horne who ran half the length of the pitch before touching down.
For Glasgow the match provided only pride to be gained. Already unable to progress in the Heineken Cup after collating a miserable two points from their first five matches, Townsend made 10 changes to his squad following their match at Ravenhill against Ulster last week, including the return of Stuart Hogg at full-back.
Ulster guaranteed themselves a home tie in the quarter-finals as they claimed a scrappy 9-8 victory over Castres at Stade Pierre-Antoine.
Although not at their best, they came from behind to win, courtesy of three Ruan Pienaar penalties.
Castres had led early on thanks to a well-worked try from Piula Faasalele but it was Mark Anscombe's side who took home the points.
Montpellier ensured they would join Toulon in the Heineken Cup quarter-finals as they cruised to a 23-3 victory over their off-colour opponents.
Tries from Thomas Combezou and Benoit Paillaugue, who converted both and also booted three penalties, gave the home side the victory they knew would assure them of a place in the last eight for the first time in their history.
Jonny Wilkinson kicked an early penalty for Toulon.
Wales Six Nations squad member Lloyd Williams was the star of the show as Cardiff Blues rewarded the dedication of their fans with a 26-14 win over Sale in the Heineken Cup.
Droves of Blues supporters had answered a plea from the region by turning up on Friday and then again on the morning of the match to clear thick snow off the Arms Park pitch.
Their sterling efforts paid off, with the Pool 6 clash able to go ahead following pitch inspections at 9am and 12 noon.
There was nothing on the match in terms of qualification for the knock-out stages, but the Blues had no wish to go through their Euro campaign without a victory and proceeded to gain revenge for their narrow defeat away to Sale back in October.
Scrum-half Williams was the key man, scoring a fine individual try and setting up another for replacement lock Michael Paterson, with Wales full-back Leigh Halfpenny kicking 16 points, as touchdowns from visiting front row forwards Tommy Taylor and Aston Croall were cancelled out.
- Sports & Recreation