Andre Esterhuizen finished what is becoming a customary comeback for Quins as the table toppers were beaten 26-20 at Twickehnam Stoop.
Freddie Burns had nudged Leicester 20-18 ahead with six minutes to go having relieved George Ford of the kicking duties, but Quins’ response was immediate as Esterhuizen showed his strength to finish in the right corner.
A first half that finished 15-12 became even tighter after the interval as Tigers showed their resilience to weather long spells of pressure before taking control.
The tide was turning in their favour when Jasper Wiese crashed over but once an exchange of place kicking between Ford and Marcus Smith subsided, the champions burst into life to engineer the decisive score.
Quins finished the Premiership title clash strongly as they kept alive their hopes of a home semi-final, but if they meet again in the knockout phase Leicester will believe their strongest line-up could finish the job.
It was a tight contest that ebbed and flowed with the start offering little idea of what was to come as Quins surged ahead as reward for choosing touch over a routine three points.
A slick line-out allowed waves of runners to push Leicester backwards and the crucial moment arrived when Alex Dombrandt broke a tackle and then popped a pass off the ground to Will Collier who touched down.
Nemani Nadolo replied with the help of some frail home defending before Quins had a Smith try disallowed for obstruction.
A play later and they were over, however, as Smith fired a bullet pass to Cadan Murley who was given a simple run in because of the speed and precision of the move.
Murley’s fearless tackle on the giant Nadolo drew a roar from the crowd and perhaps in the sign of the difficulties faced by Leicester, director of rugby Steve Borthwick walked down from the stands to the sideline to have a lengthy chat with his veteran replacement scrum-half Richard Wigglesworth.
Tigers saw an attack on the line repelled as they looked to claw back the 12-7 deficit but they had gained a foothold up front as the tempo of the game slowed.
Esterhuizen plucked a kick out of the air two handed but his clearance was poor and the mistake was costly as a counter-attack was continued by a dynamic run from Matt Scott for Hanro Liebenberg to score.
When Quins next took a scrum in front of the posts they took the points and were back in front, but the half finished with Leicester in the ascendency.
Ellis Genge and Jasper Wiese were among four Tigers forwards summoned from the bench soon after the interval and their first task was to stop the pressure building in their 22.
Once that was achieved, Leicester moved downfield and took the lead for the first time by using their forwards to pick and go until Wiese crossed.
Ford directed the conversion on to the right upright and at 17-15 the match was finely poised heading into the final quarter.
A series of scrums became fractious with Genge and Wilco Louw the source of the problem.
Louis Lynagh had a foot in touch after Smith’s clever switch of direction gave him sight of the line as Quins stepped up the attack with a Smith penalty nudging them back in front.
With points now at a premium, Ford took aim at the posts but he was wide before Burns proved successful shortly after.
The closing stages was all Quins, however, with Esterhuizen touching down and Smith adding a penalty.
Addtional reporting from PA