In a tight first half, Andy Forsyth's converted try gave the Tigers a 7-3 lead at the interval, with Rory Clegg kicking Quins' points from a penalty.
Although Clegg landed two further penalties, tries from 20-year-old winger Alex Lewington and Pienaar pulled Leicester clear to inflict Quins' fourth defeat from the last six games.
Both sides suffered exits from the Heineken Cup last week and there were multiple changes in the starting XVs.
Right from the start Leicester's fly-half George Ford was willing to let his backs run from deep and, from a Clegg touch-finder, the visitors broke out of their 22.
The Tigers spread the ball quickly for centre Forsyth to out-pace the home defence and go in under the posts, with Ford converting.
Quins responded positively in the 12th minute. A clever Clegg chip that was gathered by Luke Wallace forced Leicester to infringe at the breakdown in their 22 and Clegg had a simple kick to settle the nerves.
In the 22nd minute Clegg's attempted cross-field kick for Sam Stegmann was plucked out of the air by Tigers full-back Niall Morris, allowing Leicester to clear their lines.
Although Tom Casson and Rob Buchanan made powerful runs for the hosts it was the Tigers who looked more likely to score the next try.
And after 29 minutes winger Alex Lewington scorched through Quins' backline before offloading to Morris only for a good covering tackle to prevent a try.
The Quins coaches regrouped their side at half-time and they made a fast start to the second half with their pack earning a penalty from a scrum just outside the Tigers' 22.
Clegg slotted the points to take the home team to within a point.
But Leicester responded with their second try after 55 minutes as Lewington produced a vintage piece of wing-play. Hugging the touchline, he sent a grubber kick past Chisholm and ran around to collect and score in the corner.
Ford could not add the extras from a tight angle and Clegg kept Quins in touch with his third penalty to leave the score at 12-9.
The visitors, however, had the final say in the 68th minute when a good passing move along the Tigers' backline found Pienaar lurking by the touchline. He took two defenders with him and barrelled his way over the line.
Ford converted and despite a late missed kick from Clegg, Quins were unable to respond.
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