A fit-again Billy Vunipola will look to drag Saracens away from the abyss when the reigning European champions travel to Ospreys on Saturday.
Back-to-back defeats to Clermont last month saw the reigning two-time title-holders fall to third place in Pool 2 with the knowledge that even victories in their final two matches might not be enough to secure their passage into the quarter-finals.
And defeat in Swansea would signal a shocking early exit for Mark McCall's side.
McCall said No.8 Vunipola's performance on his comeback from knee surgery in last Sunday's 38-15 win at Wasps was "extraordinary".
"It was good to be back, I just enjoyed being out playing again and to get the win like we did was awesome as well," said the 25-year-old Vunipola, who was withdrawn after 69 minutes.
"It's good to get a great win and hopefully we can carry it into the game against Ospreys."
The Wasps success was a third in a row for Sarries following a stunning run of seven straight defeats in all competitions -- including the losses to Clermont.
Their return to form, and the added bonus of having Australian-born Vunipola and fellow England international forward Maro Itoje back from injuries, has left McCall feeling confident ahead of the trip to Wales, although he said they must maintain consistency.
"It's important that we do that against the Ospreys, that will be the biggest game of the season so far," he said.
While anything other than victory would see Sarries eliminated, French champions Clermont can book their quarters berth with a win at Northampton.
One of only three remaining unbeaten teams in the competition, injury-hit Clermont -- struggling down in 10th in the Top 14 -- will welcome back French internationals Remi Lamerat, a centre, and hooker Benjamin Kayser for their trip to already-eliminated Saints, who have lost all four group games.
- The wheel turns -
Clermont were also boosted by the news that New Zealand international full-back Isaia Toeava escaped a ban for a high tackle against Castres on December 31.
Fellow All Black and fly-half Luke McAlister is also in contention following a fractured hand.
"Maybe the wheel has turned," said Clermont coach Franck Azema about the injury crisis depriving him still of the likes of France fly-half Camille Lopez and Scotland scrum-half Greig Laidlaw.
Leinster are another unbeaten side on the verge of securing a place in the knock-out stages.
But the three-time former winners will be without three Ireland internationals against rock-bottom Glasgow in Pool 3: hooker James Tracy, centre Garry Ringrose and wing Adam Byrne. And they still have doubts over British and Irish Lions forwards Tadhg Furlong and Sean O'Brien, as well as Ireland lock James Ryan.
Pro 14 pace-setters Glasgow have already been eliminated after four straight defeats while French league leaders Montpellier travel to Exeter, the top team in England, in a must-win game for both sides if they're to stay in the quarter-final hunt.
Three-time champions Toulon host Italian whipping boys Treviso in Pool 5 looking to take control of their own destiny.
It is the tightest group so far with three teams separated by a single point.
Bath host Pro 14 champions Scarlets in the other game with the Welsh side knowing a defeat could see them eliminated if they pick up no points and both the English outfit and Toulon take attacking bonuses in victory.
Munster are the other unbeaten outfit, although they have drawn one game, and travel to Racing 92 -- finalists two years ago -- where victory would secure them top spot in Pool 4.
The top two in Pool 1 clash in Belfast where visitors La Rochelle would book their quarter-final berth with a win over Ulster, while Wasps must win at Harlequins to stay in the hunt.