Leinster handed themselves a chance of progressing to the Heineken Cup knockout stages after beating Exeter 29-20 with a bonus-point on Saturday.
The five-point win means Munster must take the maximum against Racing at Thomond Park on Sunday if they are to dump out the champions.
Leinster are currently on 20 points with 12 tries to their name while Munster sit on 15 points (9 tries) and will thus know what needs to be done when they run out to face the Parisians in Limerick.
The champions crossed the whitewash before the break through Ireland duo Gordon D'Arcy and Rob Kearney before Brian O'Driscoll went over for their third while the fourth came in the 53rd minute through imposing number eight Jamie Heaslip.
Leinster made three changes to their pack which saw Richardt Strauss join Sean O'Brien and Kevin McLaughlin as the three newcomers from last week's win over the Scarlets. O'Driscoll returned to the back line, with Johnny Sexton joined by Eoin Reddan in an international half-back partnership.
Exeter meanwhile, had sold out Sandy Park for the final home game of their first venture into Heineken Cup competition, making three changes to their side which had lost in France last week. Injuries in the back line saw Sireli Naqelevuki and Ian Whitten return to the back line, with Dean Mumm introduced to the second row.
The Irish side scored first, with inside centre D'Arcy going over on five minutes, after great tactical kicking by Sexton had earned a line-out five metres from the Exeter line.
Both sides had chosen to forgo the opportunity of points from the boot, a tactic that paid off for the home side, with Neil Clark driving over the line from a line-out maul on 17 minutes.
The Leinster forwards piled on the pressure half an hour in, for Kearney to find the line after a good back line move.
Exeter's line-out driving caused further problems for Leinster just minutes later, as referee Romain Poite awarded a penalty try for the collapse of a maul. With Gareth Steenson converting, and then scoring a penalty goal on the stroke of half-time, the Chiefs were in command at the break by a margin of 17-12.
But with two converted tries in the opening stages of the second half, Leinster got their bonus point, and although they held a nine point lead, were never fully in charge.
Steenson reduced the deficit with a penalty on 69 minutes, and as Exeter sought the try which could have earned a home win, replacement flanker Tom White was yellow carded, and Sexton scored from the penalty to restore the nine point advantage for the visitors.
Although both sides were down to 14 men with the yellow carding of Isaac Boss three minutes from the end of the game, Leinster held on for the win, but now await for Sunday's result at Thomond Park to find out if they qualify for the Heineken Cup quarter-finals.
Tries: Clark, Penalty
Con: Steenson 2
Pen: Steenson 2
Tries: D'Arcy, Kearney, O'Driscoll, Heaslip
Con: Sexton 3
Exeter Chiefs: 15 Luke Arscott, 14 Ian Whitten, 13 Sireli Naqelevuki, 12 Jason Shoemark, 11 Matt Jess, 10 Gareth Steenson, 9 Kevin Barrett, 8 Richard Baxter, 7 James Scaysbrook, 6 Tom Johnson, 5 Dean Mumm, 4 Tom Hayes (c), 3 Hoani Tui, 2 Neil Clark, 1 Ben Moon.
Replacements: 16 Jack Yeandle, 17 Carl Rimmer, 18 Craig Mitchell, 19 James Hanks, 20 Ben White, 21 Will Chudley, 22 Ignacio Mieres, 23 Nic Sestaret.
Leinster: 15 Rob Kearney, 14 Isa Nacewa, 13 Brian O'Driscoll, 12 Gordon D'Arcy, 11 Luke Fitzgerald, 10 Johnny Sexton, 9 Eoin Reddan, 8 Jamie Heaslip, 7 Sean O'Brien, 6 Kevin McLaughlin, 5 Devin Toner, 4 Leo Cullen, 3 Mike Ross, 2 Richardt Strauss, 1 Cian Healy.
Replacements: 16 Sean Cronin, 17 Heinke Van der Merwe, 18 Michael Bent, 19 Rhys Ruddock, 20 Shane Jennings, 21 Issac Boss, 22 Ian Madigan, 23 Fergus McFadden
Referee: Romain Poite (France)
Assistant referees: Christophe Berdos (France), Eric Soulan (France)
Television match official: Bernard Dal Maso (France)