The replacement flanker touched down nine minutes from time to finally shrug off a stiff challenge by the Dragons at The Rec. Rich Lane also crossed as Bath climbed to the top of Pool Two.
Dragons coach Lyn Jones was left to rue a yellow card for back-row forward Lewis Evans midway through the second half.
Evans was sin-binned on 64 minutes, handing Tom Heathcote his fourth penalty to open a nine-point lead and deny Dragons a losing point despite Toby Faletau's try.
Bath's pack then made their man advantage count when Gilbert was at the tail end of a devastating driving maul to seal the result.
Dragons remain second in Pool Two on try count, ahead of Bordeaux-Begles who picked up maximum points in their 32-20 victory in Italy over Mogliano.
- Sports & Recreation
- Tom Heathcote
- Toby Faletau