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Wasps started the brightest and earned themselves a penalty after the Irish were caught offside, with Ruaridh Jackson converting the kick for three points.
Chris Noakes then leveled the scores moments later as he slotted home the penalty kick for the hosts but Jackson had the chance to put Wasps back in front after another offside, but he missed his kick.
Jackson made up for his mistake with another three points before Frank Halai went over in the corner for the opening try of the game, but Jackson failed to hit the conversion.
However, London Irish pulled five points back on the stroke of half time after Alex Lewington made a good break before he was stopped and after Blair Cowan was denied, Johnny Williams crossed the line to score but Nokes missed the following conversion attempt.
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The Exciles pulled themselves back into the contest again moments later as Aesali Tikoirotuma lobbed the ball up and Williams was there to pick it off and cross the line to make it a seven-point game.
Wasps sealed their win late on as a rolling maul assisted Thomas Young, who forced his way across the line with nine minutes remaining.
Halai then earned his side a bonus point with his second try of the game after some good work from Daly found its way to the New Zealand international and he crossed over the line.
The win moves Wasps into fourth in the Aviva Premiership table with Leicester Tigers playing tomorrow, while London Irish remain rooted to the foot of the table.