The outcome was in the balance with Benetton holding a 21-18 advantage before Australian winger Monty Ioane dived over to finally see of the Harlequins challenge.
The Italian outfit led 18-12 at the half-time break largely to the efforts of winger Luca Sperandio who went over for a brace of touchdowns with fly-half Ian McKinley converting one and adding two penalties.
Harlequins had a dream start with flanker Alex Dombrandt finishing off some good approach work to score a try after only two minutes and he was on hand to add a second 20 minutes later with fly-half James Lang converting.
Replacement Marcus Smith landed three second half penalties to keep Harlequins well in contention but McKinley was on target to edge Benetton three points ahead before Ioane landed the decisive blow.
The sides meet again in the eagerly-awaited return at the Twickenham Stoop next Saturday.