Wasps overcame a Jacob Umaga red card to keep their Champions Cup hopes alive with a memorable victory over last season's winners Toulouse.
When Francois Cros scored after one minute, victory seemed inevitable for a visiting side packed with France stars.
But Wasps rewrote the script, taking every chance that came as first Biyi Alo then Brad Shields scored.
Despite Umaga receiving a second red card in as many months in the 33rd minute, Wasps held on to win.
Gopperth extended the hosts' lead with two penalties after the break - the second coming after Anthony Jelonch was shown a yellow card for a high tackle on Alfie Barbeary.
Pressure mounted after Peato Mauvaka scored to cut Wasps' advantage to five points with 19 minutes remaining.
Wasps held out through sheer grit and man-of-the-match Barbeary's 68th-minute try sealed an impressive win as well as a chance to claim a place in the last 16 next weekend.
Energetic Wasps defy the odds
Having lost their only other Champions Cup game this season to Munster, victory against European giants Toulouse seemed a big ask for Wasps.
But after Cros crossed, the hosts rediscovered the energy that helped them inflict Leicester's first Premiership loss of the season last weekend and heartily celebrated a turnover in Toulouse's 22.
Alo touched down shortly after and, as Wasps continued to play with nothing to lose, it looked as though Paolo Odogwu might get to celebrate his return after eight months out with a try.
The back could not quite power across the line, but Wasps did eventually win a penalty and the drive from the resulting line-out was swift and decisive as Shields scored.
Wasps did not have long to celebrate as a clash of heads between Toulouse scrum-half Martin Page-Relo and Umaga was reviewed by the TMO.
Referee Chris Busby decreed that it had been a high tackle, finding no mitigation and giving Umaga - who was returning from a two-match ban after being sent off on 26 December - another red card.
Thomas Ramos reduced the deficit to four points with the resulting penalty and Wasps were dealt further blows as number eight Tom Willis failed a head injury assessment and hooker Tom Cruse was forced from the field with a suspected shoulder injury before half-time.
TMO Brian MacNeice was called upon once again after the break when Barbeary hit his head on Jelonch's shoulder and this time the referee felt the flanker's drop in height during the tackle was enough to opt for a yellow card rather than red.
Gopperth's two penalties gave Wasps some breathing room, before Toulouse threatened a late turnaround with Mauvaka's score.
But Barbeary and Thomas Young were a nuisance at the breakdown in crucial moments and when the former scored it seemed Wasps could finally relax.
Paulo Tafili eventually made it across the whitewash for Toulouse with the clock in red but the visitors could not even come away with a losing bonus point.
With the top eight in each pool advancing to the last 16, Wasps are likely to need victory at Munster in their final group game on 23 January.
Wasps head coach Lee Blackett said: "This win would have to be up there. It's the way we won.
"That took a lot of effort. When you go down to 14 men, especially when it's someone in the backfield, you have to manage the game. How we managed the red card is the most pleasing thing."
Line-ups
Wasps: Umaga; Crossdale, Odogwu, Gopperth, Bassett; Atkinson, Wolstenholme; Martinez, Cruse, Alo, Cardall, Gaskell, Barbeary, Shields (capt), Willis.
Replacements: Frost, Nearchou, Scholtz, Carr, Young, Porter, Miller, Mills.
Red card: Umaga (33)
Toulouse: Ramos; Mallia, Guitoune, Ahki, Lebel; Ntamack (capt), Page-Relo; Baille, Mauvaka, Aldegheri, Flament, Arnold, Cros, Placines, Jelonch.
Replacements: Cramont, Neti, Tafili, Meafou, Youyoutte, Bales, Nanai-Williams, Medard.
Sin-bin: Jelonch (55)
Match officials
Referee: Chris Busby (Ireland)
Assistant referees: Keith Allen and Dave Sutherland (Scotland)
TMO: Brian MacNeice (Ireland)