The winners of the Wilcard Final on May 31 will ultimately qualify for next season's Heineken Cup, and after going down early on in this match, Leicester mounted a late comeback.
Hooker Tani Fuga and centre Mel Deane scored first-half tries for Quins, both converted by Irish fly-half Paul Burke, who added a penalty before the interval.
Leicester's sole score at that point was a penalty from fullback Tim Stimpson, but even after a quickfire second penalty from Burke for Quins just after the interval, Leicester still were not lying down.
Stimpson kicked his second penalty, before Irish wing Geordan Murphy went over for their opening try on 53 minutes, converted by Stimpson.
Burke dropped a goal and then kicked his third penalty to round off the home side's scoring, but Leicester managed a late converted try from back rower Martin Corry as well as Stimpson's third penalty.
That ensures that Sunday's tie at Welford Road has added spice, with both sides desperate to turn their mid-table seasons into a European ticket for the next campaign.
For Harlequins:Tries: Fuga, DeaneCons: Burke 2Pens: Burke 3DG: Burke
For Leicester Tigers:Tries: Murphy, CorryCons: Stimpson 2Pens: Stimpson 3