Grindlay fumbled another McLaren shot before Lilley picked up a Chris Millar pass and, from 18 yards, swept a low left-footed effort into the corner.
Paul McQuilken headed over a Scott Bannerman free-kick and David McGurn had to leap smartly to his right to deflect a goal-bound Jim Smith header as Sons battled back.
McGurn had to show sharp reflexes after the interval to prevent a Chris Boyle effort from being deflected into his own net by Scott McLaughlin. Then Lilley had a glorious run which should have brought better reward than a shot which cannoned off the junction of bar and post.
Lilley's cross was just too high for Jim McAlister and McLaren's shot was deflected over by Smith as 'Ton sought to improve their goal difference.
Dumbarton threw on an extra forward, and Scott Bannerman had a header from a Boyle corner kicked off the line by James McAlistair. From then on, it was all 'Ton.
McAlistairvolleyed over and Grindlay stood up well to save McLaren's shot, but Lilley grabbed his second when the unfortunate Smith failed to clear a Jason Walker cross and allowed Lilley to crack home from 14 yards.
Peter Weatherson put the icing on the cake when he fired in a shot from 35 yards which took a significant deflection to deceive the demoralised Grindlay.