Saracens put further pressure on Munster as they overcame Ospreys 22-15 in the Liberty Stadium, having played most of the match with 14 men.
Wales international Rhys Carre was sent off in the fifth minute for a high, shoulder-led challenge on Ospreys full-back Dan Evans at the Liberty Stadium.
It appeared a harsh call by French referee Alexandre Ruiz, who also sin-binned flanker Calum Clark before half-time, briefly reducing Saracens to 13 men.
CHAMPIONS CUP POOLS: AS THINGS STAND
But despite rugby director Mark McCall resting a host of international stars, resilient Saracens delivered a victory that means they are likely to reach the tournament's last-eight for a ninth successive season if they beat Racing 92 next weekend.
Munster are in Paris this weekend ahead of their pivotal away game against Racing 92 tomorrow.
They find themselves three points behind Saracens and defeat on Sunday will leave them perilously close to elimination in the pool phase for the first time since 2015-16.
Stuart Hogg was denied a last-minute winner against former club Glasgow as his 50-metre penalty hit the bar but a pulsating 31-31 draw edged Exeter into the Heineken Champions Cup quarter-finals.
The Aviva Premiership leaders needed only a point to secure top spot in Pool 2 and the teams shared eight tries and six points at Scotstoun.
Glasgow were left to rue yellow cards in each half, to Callum Gibbins and Fraser Brown, and two huge chances for Huw Jones which went begging in the opening five minutes of the second half.
They move on to 12 points ahead of their final game at Sale next weekend and have slim hopes of reaching the last eight as one of the three best runners-up.
Gloucester kept their hopes of a European Champions Cup quarter-final place alive with a 29-6 victory over Montpellier at Kingsholm.
However, despite the bonus point success they will probably need to secure at least a win in Toulouse in their final group game next Sunday in order to secure qualification.
This will be a daunting task as the unbeaten French side are already guaranteed top spot in Pool Five and beat Gloucester 25-20 at Kingsholm earlier in the season.
A strong second half performance disposed of a much weakened Montpellier, who were already out of the competition so chose not to select any of their France international squad members in their starting line-up.
Gloucester's tries came from Willi Heinz, Louis Rees-Zammit, Ben Morgan and Todd Gleave, Billy Twelvetrees converted three and added a penalty.
Francois Steyn and Thomas Darmon kicked penalties for Montpellier.
