Paris -Scrumhalf Dan Robson scored a try with just 58 seconds left as Wasps snatched a nerve-racking 17-14 triumph over Toulouse on Saturday to edge closer to the European Champions Cup quarter-finals.
Victory moved Wasps to second place in Pool 2, a point behind Connacht who crushed hapless Zebre 66-21.
But 2004 and 2007 champions Wasps will be favourites to grab the automatic qualifying place as their final group match next weekend will be at Zebre who have lost all five games, shipping 290 points in the process.
Connacht, meanwhile, have to travel to four-time champions Toulouse where both sides will still be in contention to make the last-eight as one of three best runners-up.
Trailing 14-10 with under a minute left on Saturday, Robson scored a wonderful smash-and-grab try by taking a quick penalty five yards out and diving over.
Toulouse had appeared to have sealed victory when they were awarded a controversial 72nd-minute penalty try for Danny Cipriani entering from the side.
Cipriani was yellow-carded and Wasps, who had fought their way back into the lead through a solo try from Elliot Daly, were looking at a nervy final weekend before Robson came to the rescue.
Connacht had stayed on course for the quarter-finals with a 10-try home win over Zebre.
Tiernan O'Halloran, Kieran Marmion and Matt Healy scored two tries each with John Cooney, Finlay Bealham, Craig Ronaldson and Caolin Blade also grabbed scores.
Later Saturday, Munster, the 2006 and 2008 champions, can book a quarter-final spot for the first time in four years if they beat Pool 1 rivals Glasgow.
Munster go into the game with a three-point lead over the Scottish side who have never reached the quarter-finals.
Two-time winners Leicester, who started the day eight points behind Munster, were facing last season's runners-up Racing 92 who have lost all four matches.
Three-time winners Leinster raced into the quarter-finals Friday with an eight-try, 57-3 humiliation of Montpellier who had Springboks star Francois Steyn red-carded for a sickening tackle on Jonny Sexton.
The Irish side, champions in 2009, 2011 and 2012, ensured top spot in Pool 4 on 21 points with a trip to Castres to come next week where they will aim to guarantee a home tie in the last-eight.
Castres' hopes of making the next round ended on Saturday with a 28-21 home defeat to Northampton.
Leinster were already 14-3 ahead by the 26th minute thanks to tries from skipper Isa Nacewa and flanker Jack Conan.
But Montpellier's hopes were dashed when 2007 World Cup winner Steyn was sent-off for a head-high dangerous tackle on Irish flyhalf counterpart Sexton.
While Sexton lay pole-axed on the ground, the bearded 29-year-old Steyn, who had kicked the French side's only points, was red-carded despite his protests.
Nacewa popped over the resulting penalty before Leinster grabbed their third try of the first half through flying winger Adam Byrne who sprinted over for his third try in the tournament this season.
The onslaught continued after the break with Conan adding the fourth try just before the hour mark, bullying his way past four defenders to score under the posts.
It gave Leinster the bonus point with Sexton adding the extras for good measure against a weary-looking Montpellier.
Conan went on to complete his hat-trick later in the half with Luke McGrath, Cian Healy and Garry Ringrose also scoring for a rampant Leinster.
"It felt like I had been hit by a forward," said Sexton as he recalled the collision with Steyn.
"I know Frans, he's a good guy and not a dirty player. I felt for him. It may have been accidental but with the rules these days you can't afford to be reckless."