Buoyed by an outstanding performance from number eight Chris Hala'ufia and 20 points from the boot of Tom Homer, they turned around a 16-11 deficit to finish comfortably on top.
Wasps were disappointing, being outgunned up front where they badly missed the firepower of number eight Billy Vunipola and failed to take advantage of Hala'ufia's spell in the sin-bin.
With this win Irish will be strong favourites to avoid the drop as they have fellow strugglers London Welsh, Sale and Worcester as their three remaining home fixtures.
Irish recalled Hala'ufia and Ofisa Treviranus to the back row while Vunipola was absent for Wasps having picked up a knock during England training. The visitors also made two further changes from last week's starting line-up with centre Elliot Daly and prop Will Taylor being introduced.
Wasps were penalised at the first ruck allowing Homer the chance to put Irish ahead but his penalty rebounded back off a post. Minutes later the full-back was given an easier opportunity and this time he made no mistake.
Irish continued to be the livelier side and were unluckily denied the first try, firstly the television match official ruled that Halani Aulika had been held up following a five-metre line-out drive and then he adjudged that Christian Wade had denied Marland Yarde a score by forcing him into the in-goal area. Yarde probably should have scored had he gone low for the tryline.
After 13 minutes, Homer extended the Irish lead with a simple penalty before Stephen Jones had Wasps' first chance for points but he was wide with his penalty attempt.
A Jones penalty put Wasps on the scoreboard before a quick piece of thinking from Ian Humphreys saw Irish score the first try. They were awarded a penalty in front of the visitors' posts which the alert Humphreys took quickly to enable Shane Geraghty to force his way over for a try which Homer was unable to convert.
Wasps steadily grew in confidence to dominate the last 15 minutes of the half with two penalties from Jones reducing the arrears before Wade put the visitors in front by evading two tackles to squeeze in at the corner for a try which Jones converted.
Just before half-time Homer kicked his third penalty but Irish still trailed 16-14 at the break.
Soon after the restart, Irish suffered a double blow when Hala'ufia was yellow-carded for a dangerous challenge on hooker Rhys Thomas with Jones kicking the resulting penalty.
Irish did not suffer in the absence of Hala'ufia however as the only score during that period was a fourth penalty from Homer. However, on his return, Hala'ufia immediately inspired Irish, making a powerful run to send Treviranus away to create a try for Yarde which Homer converted. Homer then kicked another penalty to give the hosts a 27-19 lead going into the final quarter, and despite a few late positional changes from Wasps as they tried to recover, Homer made the points safe for the Exiles with a late penalty.