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 with a Neil Clark score, a penalty try and 10 points from the boot of Gareth Steenson the reply for Exeter.
Ulster improved their chances of a home tie in the quarter-finals with 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 and now await results on Sunday to see if they will have home advantage in the last eight.
Glasgow put an end to Northampton's hopes of progression as Peter Horne's last-gasp try secured a 27-20 victory at a frosty Scotstoun Stadium.
Lloyd Williams was the star of the show as Cardiff Blues defeated Sale 26-14 - their first Heineken Cup victory of the season.
Unbeaten Clermont Auvergne booked a home draw in the 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.
Montpellier ensured they would join Toulon in the next stage as they cruised to a 23-3 victory over their off-colour opponents.