Leicester set up a mouth-watering final round clash against Toulouse after a dramatic 15-15 draw with Ospreys in European Cup rugby on Sunday, a result that ensured that no Welsh province will make the knock-out phase.
Four-time champions Toulouse notched up a bonus-point 35-14 victory over Italian whipping boys Treviso to sit atop Pool 2 on 18 points.
Leicester, themselves twice champions, are just two points adrift and will host the French giants at their Welford Road ground next week knowing that nothing but a win will suffice.
Two-time champions Munster earlier kept their hopes of reaching this season's quarters alive with an unimpressive 26-17 win over pointless Edinburgh.
Victory saw Munster go second in Pool 1, three points behind Saracens, with one match remaining next weekend when the English side should seal top spot and a place in the last eight when they play Edinburgh.
Munster, whose last eight hopes probably rest in getting one of the two best-placed runners-up spots, host third-placed Racing-Metro in Limerick next Sunday.
Harlequins, Ulster and French duo Toulon and Clermont have already secured their berths in the knock-out phase.
At Swansea's Liberty Stadium, Ospreys playmaker Dan Biggar missed three penalties in the first 16 minutes, two coming back off the woodwork.
The wannabe Wales fly-half finally nailed one and then landed a conversion to a stunning try by No.8 Joe Bearman after a series of smart offloads from captain Kahn Fotuali'i, flanker Justin Tipuric and prop Ryan Bevington.
Toby Flood pulled back a penalty to make it 10-3 at half-time.
Biggar saw another penalty come back off the posts as Leicester upped the pressure, scrum-half Ben Youngs eventually crossing for a try Flood converted to draw the Tigers level.
Niall Morris then pulled off a fantastic finish past Eli Walker to cross in the corner as Leicester turned the screw.
An electrifying run by Walker saw Ospreys fire straight back, replacement Jonathan Spratt crossing for a similiarly smart finish in the corner at the other end of the pitch.
But Biggar missed the conversion to hand the Tigers a chance to advance next week, and again condemning the four regions from the reigning Grand Slam champions to the sidelines.
"We came here to win, and the overriding feeling is one of disappointment," said Tigers scrum-half Youngs. "Luckily Dan missed the kick at the end there.
"We're really disappointed. Next week's a bigger game again, there's everything to play for."
Toulouse ran in five tries against Treviso through South African hooker Gary Botha, Argentinian lock Patricio Albacete, Vincent Clerc, Florian Fritz and Yoann Huget, the Italians managing a memorable length-of-the-pitch five-pointer from Tommaso Benvenuti.
Munster looked to be cruising when they scored two tries in quick succession in the second-half against Edinburgh, but the hosts hit back with a brace of tries of their own, both through wing Dougie Fife.
But the Irish province held on and also deprived the Scottish side of a losing bonus point as last season's semi-finalists remained pointless with a game to play.