Jacob Umaga was sent off in the 33rd minute of the victory.
They had (14) 30.
Tries: Alo, Shields, Barbeary; Pens: Gopperth 3.
Toulouse: 22.
Tries: Ramos 2 and Tafili.
A red card for Jacob Umaga was not enough to prevent a victory for Wasps over Toulouse.
When Francois Cros scored after one minute, victory seemed inevitable for the visiting side.
The script was rewritten by Wasps, who took every chance that came as first Biyi Alo then Brad Shields scored.
In the 33rd minute, Umaga was sent off for the second time in less than a year, but that was not enough to stop the win.
Gopperth kicked two penalties after Anthony Jelonch was shown a yellow card for a high tackle.
After Peato Mauvaka scored to cut the deficit to five points, pressure mounted.
The man of the match was Barbeary, who scored the try that sealed the win and gave the team a chance to make it to the last 16.
The Energetic Wasps defy the odds.
It was a big ask for Wasps to beat Toulouse in the European competition.
The energy 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611 888-270-6611
It looked as though Paolo Odogwu might get to celebrate his return after eight months out with a try as the team continued to play with nothing to lose.
The back could not power across the line, but the drive from the resulting line-out was decisive as Shields scored.
A clash of heads between Toulouse scrum-half Martin Page-Relo and Umaga was reviewed by the TMO and was not good news for Wasps.
Umaga was sent off for a second time after the referee Chris Busby ruled that it was a high tackle and gave him another red card.
The deficit was reduced to four points with the help of a Thomas Ramos penalty, but the damage was done before the half-time whistle as number eight Tom Willis failed a head injury assessment and hooker Tom Cruse was forced off with a suspected shoulder injury.
After the break, Brian Mac Neice was called upon when Barbeary hit his head on Jelonch's shoulder and the referee decided to give him a yellow card rather than red.
Gopperth's two penalties gave Wasps some breathing room, before Toulouse threatened a late comeback.
When Barbeary scored, it seemed that the team could finally relax.
The clock was red but Toulouse could not get a losing bonus point.
In their final group game on 23 January, Wasps will need to win at Munster to advance to the last 16.
Line-ups.
Crossdale, Odogwu, Gopperth, Gopperth, O'Brien, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale, Crossdale,
Replacements: Nearchou, Carr, Young, Porter, Miller, and Frost.
Umaga had a red card.
Toulouse: Ramos, Mallia, Guitoune, Ahki, Lebel, Ntamack, Page-Relo, Baille, Mauvaka, Aldegheri, Flament, Arnold, Placines, Jelonch.
Replacements: Neti, Tafili, Youyoutte, Bales, and Medard.
Jelonch has a sin-bin.
Match officials.
Chris Busby was the referee.
The assistant referees are Dave and Keith Allen.
Brian Mac Neice is from Ireland.