The win came at a cost however as scrum-half Joe Simpson, one of the 18 players released from England's RBS 6 Nations training squad, dislocated his left shoulder in the first half.
But Wasps overcame the setback to move eight points clear of bottom club Newcastle Falcons with a victory which could rescue their season.
Fly-half Nicky Robinson kicked all their points with six penalties from seven attempts.
Irish replied with the only try of the match from Fijian winger Sailosi Tagicakibau, with fly-half Steve Shingler landing the conversion and two penalties.
Simpson's 27th-minute injury appears a bigger blow for Wasps than England with the London club still battling for Premiership survival.
The injury to Simpson, who was replaced by Nic Berry, was the latest for Wasps, who have lost an entire side to injury this season.
Former England stars Joe Worsley and Steve Thompson, along with Dan Ward-Smith, have been forced into retirement, while they lost England centre Riki Flutey for the rest of the season two weeks ago, followed by lock Marco Wentzel last week.
Robinson missed a 10th-minute penalty but made amends to kick his side ahead with a second chance three minutes later.
Shingler equalised with a penalty but Robinson kicked Wasps back in front after the Exiles were penalised at the breakdown.
Another Shingler penalty in the 29th minute drew Irish level for the second time, but the fly-half failed to put the visitors ahead when he missed a simple penalty late in the first half.
Wasps had their share of attacking opportunities in the first half but squandered the best two.
After dragging Delon Armitage into touch, they wasted an attacking lineout when hooker Rob Webber, released by England along with Simpson, misdirected his throw into the line.
Then, with their forwards forcing the visitors to defend desperately in front of their own posts, they were penalised at an attacking ruck.
Wasps appeared to have suffered another injury blow just before half-time when centre Dominic Waldouck limped off with a leg injury, but he reappeared for the second half with his left knee strapped.
Wasps maintained the pressure and, when Irish were caught offside, Robinson landed his third penalty from 40 metres to put the home side ahead for the third time.
The half-time introduction of the more experienced Ben Broster for Simon McIntyre at tighthead strengthened the Wasps scrum and a huge push forced Irish to concede a 59th-minute penalty which Robinson kicked to extend their lead to six points.
But the good work was undone when a defensive lapse allowed Exiles winger Tagicakibau to score his side's 66th-minute try.
Following a lineout, centre Jonathan Joseph released the Samoan who evaded Tom Prydie and full-back Hugh Southwell to cross in the corner.
Shingler landed the difficult conversion but determined Wasps retaliated.
A downfield kick from Robinson bounced well for teenage centre Elliot Daly, who kicked as he was tackled and Jack Wallace and Waldouck set off in pursuit, but Irish replacement Darren Allinson scooped the ball behind his own line.
The now dominant Wasps pack won a penalty at the resulting scrum, allowing Robinson to kick them back in front after 72 minutes, and he hit the target again when his forwards were awarded another at the next scrum three minutes later.
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