The reigning Aviva Premiership champions ended Biarritz's four-year unbeaten home run in the competition to wrap up a dominant display in the pool stages.
Tom Guest grabbed the game's only try while the tactical and goal-kicking of Nick Evans, who scored 11 points, proved decisive.
Defeat ended Biarritz's slim hopes of progressing, though the 2006 and 2010 finalists could still qualify for the Amlin Challenge Cup as one of three group runners-up.
Harlequins had previously found tries easy to come by in Europe though head coach Conor O'Shea will have been satisfied at his team's professional display, despite a second successive yellow card for England prop Joe Marler.
Biarritz had only lost one of their last 35 European games at Parc des Sports Aguilera and none since 2008 but Quins rarely looked like losing this tie.
The visitors were under pressure early on and conceded the opening points of the game but responded to lead 10-3 at half-time in heavy and wet conditions in south-west France.
Ollie Kohn produced a crucial turnover as the Biarritz pack rumbled towards the line as early as the fifth minute and Dimitri Yachvili fired wide before kicking Biarritz ahead on 12 minutes.
But Quins and Evans swiftly adapted to the conditions to turn the tables on their hosts.
Evans' cross-field kick to Ugo Monye almost opened space for Mike Brown, making his 200th club appearance, but was denied by Wales wing Aled Brew.
Takudzwa Ngwenya then coughed up Evans' hoisted kick and Danny Care kicked Quins up-field.
Iain Balshaw scurried across to snuff our the danger but from the resulting lineout, number eight Guest came down with the ball and slipped from his opposite number's hands to charge over from 10 metres out.
Evans converted for a seven-point lead after half an hour that Biarritz struggled to impact upon.
Both sides finished the half with 14 men when Joe Marler, for the second game in a row, and Wenceslas Lauret were ordered to the sin bin for trading blows.
Quins appeared comfortable but indiscipline undermined their efforts and allowed Biarritz to remain within touching distance.
Brown was penalised after he was collared deep inside his own half early in the second half to hand Yachvili his second penalty.
James Johnston then conceded for an infringement at a scrum, despite Harlequins' obvious advantage, and Yachvili narrowed his side's deficit to a single point on 54 minutes.
Marler then made amends for his earlier dismissal by winning a penalty for his great work at the breakdown after fellow yellow card subject Laurent was tackled and Evans saw his speculative effort from half-way bounce over off the crossbar.
Harlequins blew an attacking lineout for obstruction but escaped further punishment moments later when Yachvili pushed his effort wide.
Evans had no problems with a third penalty from distance while Harlequins' advantage at the scrum then helped count down the final minutes to a well-deserved win.
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