The Tigers had Andy Goode – restored to the starting line-up after recovering from a knee injury – to thank for all their points with the in-form fly-half converting five of his eight penalty attempts.
Goode's opposite number Jeremy Staunton weighed in with three penalties to secure Quins a losing bonus point, but that will be scant reward for a team on their worst Premiership run of eight consecutive losses.
Quins boss Mark Evans could certainly take heart from the fire shown by his players but there was little else for him to cheer following a display desperately lacking in invention.
Their pack toiled admirably up-front but were always out-muscled by Leicester and although the wet conditions hardly helped their cause, their failure to create a single try-scoring chance told its own story.
Leicester created little more however – they had a sniff of the line on just two occasions – and they seemed content to use Goode's kicking game to play for territory and take the points on offer when they came.
Much of the early excitment came from some heated exchanges betwen the two sides.
Tigers prop Julian White and Quins hooker Tani Fuga traded blows and moments later locks Martin Johnson and Simon Miall were given a warning by referee Dave Pearson for a minor skirmish.
Two penalties from Goode sandwiched three points from Staunton's boot as Leicester shaded the opening 10 minutes on the scoreboard, although for much of that time they were forced onto the defensive by Quins' aggressive running.
Goode punched a big hole in the home defence with a powerful break after 19 minutes that swept him up to the 22, but his fine work was squandered by a loose pass which fell into the arms of Quins winger Simon Keogh.
Leicester continued to pile on the pressure and were rewarded by a third Goode penalty but Staunton reduced the deficit once again following a quick-fire raid deep into the Tigers' half.
Former England flanker Neil Back was sent to the sin-bin after 30 minutes for using his hand in a ruck and Staunton made no mistake with the ensuing shot at goal to level the score 9-9.
Seru Rabeni slipped through Quins' line and only had fullback Gavin Duffy to beat but the ball squirted out of the big Fijian's hands from metres out as the driving rain began to take its toll.
There was still enough time in the first-half for Goode to boot another penalty and the Tigers retained the initiative shortly after the interval when Goode stroked over three more points.
Evans' men enjoyed some promising spells in the third quarter, using two rolling mauls to barge their way into enemy territory but on both occasions their forwards ran out of steam.
Leicester were pegged back close to their own whitewash in the 55th minute but excellent work at the line-out saw them escape unharmed leaving Quins, lacking the ideas or strength to break through, frustrated.
Neither side could make any headway in the final quarter as play was interrupted by a sea of errors and the final whistle was welcomed by the sell-out crowd whose jeering summed-up the game.
For Harlequins:Pens: Staunton 3
For Leicester:Pens: Goode 5