It was Greenwood in fact who opened the Quins’ scoring on 35 minutes when he went over for a try, cancelling out an early penalty from Bath’s Olly Barkley.
Wing Matt Moore was next over for the home side just before the break, giving his side a 12-3 advantage at the break.
Barkley got back within three points just after half-time with his second and third penalties of the match, but two in reply from Australian fullback Nathan Williams put the seal on the match.
HarlequinsTries: Greenwood, MooreCon: WilliamsPens: Williams 2
BathPens: Barkley 3