At half-time Wasps held a slender 13-9 lead as a penalty try and the boot of veteran Andy Goode cancelled out two penalties from James O'Connor and one from Shane Geraghty.
And, although Goode, who finished the match with 14 points, and O'Connor traded kicks after the interval, experience won over youth as the visitors held on, condemning the Exiles to their six straight loss in all competitions.
Wasps ended a run of three consecutive defeats by winning a first Aviva Premiership match in Reading since March 2008.
Irish started well, claiming the kick-off and opening the scoring inside three minutes through an O'Connor penalty.
However, Wasps responded immediately as they won a line-out just inside the Exiles' 22 and put pressure on the Irish defence through a rolling maul which led to a penalty which Goode converted.
With both sides in the midst of losing runs, the opening 20 minutes saw both teams struggling to find a passing rhythm, with further penalties from Goode and O'Connor leaving the score at 6-6.
Wasps had the majority of possession and territory in this period, but handling errors and strong defence by the hosts prevented them from creating any real scoring opportunities.
However, Wasps began to stretch the Irish defence and they were awarded a penalty try on 35 minutes.
Goode chipped a cross-field kick which bounced awkwardly for O'Connor, who deliberately knocked-on with Elliot Daly waiting to pounce. O'Connor was sin-binned and Goode converted to give the visitors a 13-6 lead.
Shane Geraghty converted a penalty on 38 minutes to reduce the gap to four points heading into half-time.
But Goode restored Wasps' seven-point lead three minutes into the second half.
O'Connor's return after 44 minutes coincided with some good pressure from the Exiles.
Ojo, playing his 200th match for the club, almost managed to break through the Wasps defence and a few phases later O'Connor was brought down just short of the visitors' try-line.
The ball was recycled, but a knock-on 10 metres out prevented an opportunity emerging.
This gave the hosts confidence, with Geraghty breaking from his own half up to the Wasps' 10-metre line, but his kick ahead was claimed by Daly before the chasing runners could reach it.
With 15 minutes to go O'Connor converted a penalty to reduce the gap to four.
A minute later Christian Wade, in his first game since November 2, was penalised for holding on and O'Connor attempted another kick from 35 metres near the touchline, but saw it drift slightly to the right.
The momentum was now with London Irish and they found themselves camped inside the Wasps half, but the visitors' defence were holding firm.
And Wasps were given some breathing space by the trusted boot of Goode as he sent a drop goal over just three minutes from time.
The kick helped put a smile back on Dai Young's face as just before the Wasps director of rugby saw Wade limp off the pitch with an ankle injury.
To their credit Irish did not give up and spent the last two minutes camped on the Wasps try line.
With time up Wasps' Charlie Hayter was sent to the sin bin after a number of penalties but Will Helu got his hands on the ball and cleared to touch to secure the win.