Victory moved the Sharks to second in Pool Five, a point behind Toulouse, while the Quins are already eliminated after four straight defeats.
The match only went ahead after volunteers were brought in to clear the snow from the pitch, and Sale took full advantage – Fijian Sisa Koyamailbole touching down to give his side an early lead.
The Quins forced their way back, however, with Nick Evans converting his own try to put the visitors in front before Aston Croall stretched the lead to nine points with his converted score.
Two Charlie Hodgson penalties either side of the break cut the deficit to three before Sale hit the front through Eifion Roberts’ converted try.
The match was almost abandoned with ten minutes left due to the wintery conditions, but once the game resumed after a debate, Hodgson ensured there would no late twists, cancelling out Evans’ penalty to wrap things up.
Gloucester, meanwhile, produced a stunning second half display to recover from 6-0 down to beat Glasgow 19-6 in Pool Two.
Nicky Robinson kicked three penalties, while Charlie Sharples and Alex Brown touched down as Gloucester avenged last weekend’s 33-11 defeat in Glasgow.
Irish giants Munster produced a tremendous away display to beat French champions Perpignan 37-14 to take charge of Pool One.
It was Perpignan’s first home defeat in Europe since Wasps beat them five years ago – a run stretching 16 matches.
French side Stade Francais beat Ulster 29-16 to resume control of Pool Four.