Neither side was able to claim any early advantage and it was a full 24 minutes before a clear chance was created and with this came Thistle's opener.
A Ricky Gillies corner was met by Mark Roberts and his header was cleared for another corner but when Gillies' cross was again met by Roberts, his overhead kick from 10 yards crept inside the far post.
Dumbarton were creating very little but with only three minutes left in the first half they almost equalised when John Gemmell squared to Paul McQuilken who blasted his shot over the bar from 16 yards.
The second half began as the first had ended with Dumbarton in the ascendancy and Ryan Borris was unlucky on 48 minutes when his shot was blocked and cleared for a corner.
After this Thistle regained control of the match and they doubled their lead on 61 minutes when Stephen McConalogue beat Dumbarton's offside trap and ran fully 30 yards before calmly slotting the ball under the onrushing keeper.
To their credit Dumbarton came back into the game and in the 90th minute Gemmell had a chance for a consolation but his six-yard shot was well saved by Kenny Arthur.
The visitors did get a consolation four minutes into injury time when Andy Rodgers was adjudged to have been brought down by Stevie Nicholas and, although Iain Russell's spot-kick was saved by Arthur, Chris Boyle was on hand to tap in the rebound.
After Saturday's disappointment this was a welcome three points for Thistle, but Dumbarton now find themselves languishing near the relegation zone at the bottom of the league.