Quins thoroughly deserved their 23-16 success after dominating the Aviva Premiership champions for much of the game and scoring two tries, through former England number eight Nick Easter and centre Matt Hopper.
Full-back Nick Evans converted both and also kicked three penalties, while Leicester scored a penalty try in the 80th minute, which was converted by fly-half Owen Williams who also kicked three penalties for the Tigers.
Harlequins' win meant they leapfrogged Leicester in the table and will lead to much soul searching at the Tigers who have now won just one of their past five matches in all competitions.
The defeat was only Leicester's second in all competitions at home since September 2012.
Both sides were badly hit by international calls and injuries, forcing Leicester to field many of their second string players, including both half-backs.
Harlequins fielded centre Tim Molenaar, on loan from Gloucester, Easter moved into the second row and fly-half Evans played full-back.
Harlequins, fresh from a win over Sale which ended a four-match losing run, dominated the first half and turned around with a 10-6 lead which could easily have been more but for a glut of errors which ruined promising build-up play.
At one point they had conceded nine penalties to Leicester's one, forcing referee Tim Wigglesworth to warn captain Easter about their future conduct.
Those penalties allowed Leicester to take a 6-0 lead but Harlequins' better play was eventually rewarded with a try under the posts by Easter in time added on.
Leicester had the benefit of a strong, swirling wind in the first half and Welsh fly-half Williams took full advantage by drilling two long-range penalties straight between the posts in the eighth and 18th minutes. He was also close with a third.
Quins twice turned down shots at goal because of the wind and went for the line-out and drive option but failed to take advantage due to their poor execution, not the least dropped passes.
Such was Harlequins' dominance that it took Leicester 28 minutes to get into the visitors' 22, and that was thanks to a long clearance by flanker Julian Salvi.
Leicester failed to take advantage and after Evans had put Quins back in the game with a 37th-minute penalty, the full-back almost scored in the left corner but was denied by some great scrambling defence by the Tigers.
Leicester won the line-out but conceded a scrum and Quins, for once, took advantage of a strong attacking position when Easter drove over from close range, with Evans slotting the conversion.
Harlequins made a brilliant start to the second half and after fly-half Ben Botica missed a long-range penalty, centre Hopper cut inside off the left wing and darted under the posts, with Evans adding the conversion.
That put Quins 17-6 ahead, which soon became 17-9 after Williams kicked his third penalty.
With a 24,000 sell-out crown finding their voice, the Tigers suddenly discovered another gear and Harlequins found themselves under the cosh after a clearance kick was charged down.
But Leicester failed to change the scoreboard and when Quins broke out of defence they won a penalty in the Leicester 22 and Evans made it 20-9.
In the 73rd minute the Kiwi kicked his third penalty to make it 23-9 but Leicester hit back with a penalty try, converted by Williams, in the final minute.
- Sports & Recreation