London Irish (10) 22 Tries: S Armitage, Mapusua, D Armitage Cons: Hewat 2 Pen: Hickey
Tom Varndell is tackled by Delon Armitage at Welford Road
Leicester made it two wins from two games in the Premiership - but only after full-back Peter Hewat missed a last-gasp conversion for London Irish.
Trailing 24-17 with two minutes left, Delon Armitage went over for the Exiles only for Hewat to hook his kick wide.
The sides were 10-10 at the break, Geordan Murphy crossing for the hosts and Steffon Armitage scoring for Irish.
Seilala Mapusua put the Exiles in front only for Tom Croft and Ben Herring to claim the vital tries for Leicester.
Irish, who lost influential lock Nick Kennedy before the match because of illness, continued where they left off against Wasps last week and made the early running at Welford Road.
They were denied an early try when Herring stopped winger Sailosi Tagicakibau going over, but they eventually opened the scoring on 10 minutes when new signing Toby Flood released Murphy for his second try in two games.
Irish responded with a monster penalty from Hickey and a try from flanker Armitage.
England half-back Flood missed his second penalty of the day but pulled the scores level with a successful attempt just before the break.
Irish were gifted their second try when Mapusua charged down Murphy's kick before picking up the loose ball and diving over.
But Herring's perfectly-judged grubber kick gave Croft the chance to gather and score before Flood's touchline conversion levelled the match again at 17-17.
The Tigers took the lead when Herring held off the Exiles defence to score under the posts.
Armitage then looked like earning his side a draw with a stunning try after 78 minutes, but Hewat missed the crucial kick from the touchline.
Leicester head coach Heyneke Meyer: "When we were a try up, we should have finished the game off and we need to work harder on our game management.
"They preyed on our mistakes and we put ourselves under pressure.
"I am not happy with the performance. There are a lot of areas that we need to improve. They pushed us very hard in midfield. We will need to work very hard on Monday.
"It was a win but there is still a very long way to go. We should have scored more tries.
"It will take time for us to adapt to the interpretation of the rules but that is no excuse - we should have dealt with that better. I will always take an ugly win over a pretty loss."
London Irish boss Toby Booth:
"When you put yourself into a position to win the game, it's tough when you don't win.
"You make it difficult for yourself if you don't win your own ball and you have to try and find other ways of getting into attacking positions.
"We only won a third of our ball but we have run a very, very good side very close. We were very good last week and we were nearly very good this week. We are trying to adopt a ruthless streak and we need to do that if we want to win trophies.
"Welford Road is a very difficult place to come. But we have beaten everyone in the past three years and mentally, it's important that we come over those hurdles."
Leicester: G Murphy; Varndell, Hipkiss, Mauger, Smith; Flood, Ellis; Ayerza, Chuter, White, Blaze, Kay, Croft, Herring, Crane. Replacements: J Murphy for Hipkiss (50), Dupuy for Ellis (59), Kayser for Chuter (50), Cole for White (54), Wentzel for Blaze (25), Woods for Herring (76).
Not Used: Vesty.
London Irish: Hewat; Ojo, D Armitage, Mapusua, Tagicakibau; Hickey, Hodgson; Lea'aetoa, Coetzee, Rautenbach, Rouse, Johnson, Thorpe, S Armitage, Hala'ufia. Replacements: Richards for Hodgson (52), D Murphy for Lea'aetoa (41), Paice for Coetzee (58), Fisher for Rouse (52).
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