The Tigers looked comfortable and even turned down kickable penalties in search of tries as they lead 24-7 with just a quarter of the match left.
But Irish dug deep and, in a magnificent finale, they became the latest side to come away from the Leicester bearpit with points.
It was the Tigers' first home Premiership fixture this season with their World Cup players available and, after a string of losing results so far that has plunged them to the bottom end of the table, they were desperate before kick-off to add to the 34-13 away thumping they delivered to Sale Sharks last week.
Irish, meanwhile, had every incentive to win and bounce back from a 13-12 home loss to Bath.
Leicester were out of the blocks quickest but it may have been early nerves for returning England fly-half Toby Flood as he missed a sitter of a penalty from 25 metres after the Tigers had taken a scrum against the head and put Irish under pressure.
Flood made up for that miss with a simple penalty moments later but the lead did not last long as Irish hit back with the first try of the match.
It was a neat drive down the right to the home 22 before the ball went inside for Jebb Sinclair, who fed England centre Shontayne Hape and the ex-Bath back rounded the last defender to score.
Full-back Tom Homer converted but Irish found themselves a man down on 20 minutes when captain Dan Bowden was sin-binned for holding on in a ruck illegally.
The Tigers opted for the scrum and, with a man in the pack withdrawn, the home eight had Irish on the back foot, eventually getting a penalty try when a set-piece collapsed.
Leicester's scrum was pretty dominant in the opening half, and Irish were left fighting to hold their own.
The closest Irish came to scoring again was a Homer penalty from 51 metres, just inside his own half, which dipped under the crossbar.
It was not all one-way traffic, however, as the Exiles' defence stood firm and as the half wore down they held the Tigers to between the 22 and the halfway line.
But just as Irish would have been satisfied to have gone into the break just three points adrift, they gave away another penalty in front of the posts which Flood gratefully accepted.
A third Flood penalty took Leicester two scores ahead and they looked set to go up another gear. Yet Irish found renewed heart and came close to crossing for a try twice.
Leicester were having none of it and hit back with another Flood penalty. Now, with confidence oozing through them, the Tigers went for try.
Just after the hour mark they got it when flanker Tom Croft went driving for the line but it found centre Horacio Agulla.
Gritty Irish would not lay down, however, and from a situation where they looked like going home with nothing, they clawed their way to at least losing bonus point range.
Replacement wing Adam Thompstone scampered over from 20 metres on the left after some excellent work by his team-mates which Homer booted magnificently from near the touchline.
And then the young full-back added a 30-metre penalty in front of the posts, after the Tigers had infringed, to put his side seven points behind.
Irish pressed again for their crucial third try of the match with the minutes running out.
Dramatically, the Exiles won a penalty, kicked for touch close to the Leicester line and, when the Tigers took the ball and threw it back, Flood's clearance was charged down for replacement Matt Garvey to leap high, catch and ground in the right corner.
Homer kicked a golden touchline conversion to level the game but Leicester had one last chance to win it after the clock turned 80 minutes.
Yet Flood skewed a 25-metre drop goal wide of the uprights and Irish escaped with a draw.
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