Harry Potter chased down Ben Youngs’ kick ahead to score the first try.
Quins’ Louis Lynagh cut the Tiger’s lead to 16-14. However, late Quins pressure amounted to nothing and Leicester maintained their perfect start to the season.
Victory for Leicester Tigers gave them a nine point lead at the top of the Gallagher Premiership.
Leicester: Steward; Potter, Moroni, Kelly, Nadolo; Ford, B Youngs; Genge (capt), Montoya, Cole, Wells, Green, Liebenberg, van Staden, Wiese.