Leicester then scored one of the tries of the season, with a breathtaking move, started from a stolen line-out by Calum Green well inside their own half.
The ball quickly found its way to Lote Tuqiri who powered forward in a weaving run at speed before feeding Hamilton, who cut back outside to finish brilliantly in the corner.
It was a fitting tribute to Tuqiri's distinguished Leicester career in his last appearance in a Tigers shirt before he leaves Welford Road to play rugby league for Wests Tigers in Australia.
The try sent the home crowd into raptures and they would be treated to another just minutes later.
Substitute George Chuter scored the winning try for Leicester
Provider Castrogiovanni turned scorer, showing good vision to intercept a loose pass in the London Irish 22 to score under the posts.
A shell-shocked Irish did their best to claw their way back, but full-back Homer squandered two penalty chances.
Flood also missed a couple of opportunities to put Leicester further ahead, before being substituted as a precaution after suffering a blow to the head.
Irish managed to get back in the game with Armitage edging over to finish some good forward pressure.
The second half turned more into a kicking affair with Lamb converting three kicks for London Irish.
Chuter finished off another powerful move from the home side to score the winning try on 69 minutes.
Leicester head coach Richard Cockerill: "The performance in the first half was fantastic. The second half was a bit scrappy and a bit disjointed but obviously losing Toby Flood didn't help that.
"But I am delighted with the performance, we scored four tries against a good side so you can't ask for anything more than that.
"The players had a tough week on the training field after last week [a 19-3 defeat at Northampton] and mentally it's been hard for everyone.
"It was good to bounce back and five points was just what we needed."
London Irish boss Toby Booth:
"We gave ourselves a mountain to climb and we probably gambled a bit in our 22 for their fourth try which we probably didn't need to do.
"That was the killer blow in relation to losing bonus points but we have a couple of weeks off now.
"I said at half-time, amongst other things, we needed positives to take away with us because when we pick the reins up in seven days we need to have things to build on for the final furlong.
"And I think we saw that in the second half, there was something to build on, on what was a very difficult afternoon."
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