The victory sees the Tigers leapfrog Saracens back into second place, with a win against Bath in two weeks' time guaranteeing a home semi-final although they might be without England flanker Tom Croft, who went off injured in the first half at the Twickenham Stoop.
In an action-packed first half, Leicester drew first blood through Thomas Waldrom's try, only for Harlequins to race into a 23-10 advantage courtesy of two tries from Ugo Monye and Nick Easter. But Leicester ensured the game remained in the balance at half-time as Steve Mafi went over to ensure they were only three points behind.
While George Lowe's try restored Quins' advantage, Leicester went through the gears in the second half as a try from Alesana Tuilagi and Waldrom's second brought up the bonus point before Toby Flood, who finished with 23 points, rounded off the win with a late penalty.
Leicester's intentions were clear from the off as Flood turned down a shot at goal and kicked to the corner, with number eight Waldrom finishing off a catch-and-drive under a heap of Quins players, with Flood adding the extras.
The home team hit back immediately through a Nick Evans penalty and the New Zealander added a further penalty after one from Flood.
The England hopeful then had a big hand in the next try, but it was not the one he wanted, as Monye came off his wing to pick off Flood's pass before sprinting in from 60 metres. Evans' conversion put Quins 13-10 up and they were soon a man to the good as well after Manu Tuilagi was yellow-carded for pulling a home attacker and Evans added further punishment with the boot.
With momentum firmly behind the home team, number eight Easter added their third try when he went blind from a five-metre scrum to crash over with Evans' conversion taking the hosts 13 points ahead.
Croft injured himself in his attempt to halt Easter and was treated on the pitch for six minutes before being carried off.
Evans and Flood traded another penalty apiece before Leicester rallied on the stroke of half-time, first when Mafi - Croft's replacement - spotted a gap at a ruck and raced through. Flood converted and added a penalty in the final play of the half to leave the game tantalisingly poised at 26-23 to the home side.
The home team's advantage soon evaporated with Flood kicking Leicester level after the Tigers scrum earned a penalty.
But in a topsy-turvy game, Quins immediately hit back when they won a scrum against the head and centre Lowe latched onto Evans' perfectly-weighted grubber-kick and Evans converted.
There was no let-up in the action, with Quins being tested to the limit before drawing level in the 63rd minute.
Centre Anthony Allen laid the platform with a scything break before the ball was shifted to the left where Alesana Tuilagi who was not going to be stopped from close range. Flood added the extras to make it 33-apiece, and Waldrom's converted try after 70 minutes put the east midlands side in the driving seat and earned the bonus point. It was the outstanding Flood who rounded off the victory with a late penalty.
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