John Brown's men wrapped up their third victory in succession to underline their growing title credentials as Peter MacDonald grabbed a brace.
The visitors from the north enjoyed more of the possession in the first half at the Bet Butler Stadium, but couldn't turn that superiority into many clear-cut scoring chances.
Craig Beattie came closest to breaking the deadlock when he struck the bar from long range, but Dumbarton also saw a Mark Gilhaney lob bounce off the top of the upright. The breakthrough came three minutes after half-time when MacDonald's free-kick flew past Jamie Ewings, helped by a deflection.
Dumbarton's Colin Nish was then red-carded for a second bookable offence just before the hour mark and Dundee took full advantage.
Ryan Conroy fired an excellent left-foot shot high into the net to give the Dens Park outfit a two-goal cushion.
MacDonald scored his second from the penalty spot and, after Jordan Kirkpatrick had pulled a goal back for the home side, Gavin Rae rounded off a fine passing move to give Dundee victory.
Alloa Athletic and Falkirk fought out a 0-0 stalemate at Recreation Park. Scott Bain produced a man-of-the-match display in the home goal, thanks mainly to first-half saves from Phil Roberts and Blair Alston.
Neither side could take a firm grip in the second half, but Paul Hartey's side had a narrow escape when Graeme Holmes almost deflected a Craig Sibbald free-kick into his own net. Jason Marr could have won it for Alloa in the closing minutes, but headed over from close range.
Queen of the South and Cowdenbeath could not be separated at Palmerston Park, but it took a late header from Andy Dowie to give the home side a point in a 1-1 draw.
That goal spared the blushes of goal keeper Calum Antell who had let a Greg Stewart shot slip through his fingers after 11 minutes as Cowdenbeath started well.
Kenny Adamson and Kane Hemmings also had chances in the early minutes before Queens finally found their feet.
Derek Lyle was unlucky not to equalise when his lob hit the underside of the bar and he also forced a good save from Thomas Flynn shortly before half-time.
As the match wore on, an equaliser seemed more likely and Queens' Ryan McGuffie should have scored when he headed over from six yards out.
But Dowie had the final say with a powerful header, which left Flynn with no chance to deny Cowdenbeath an away win.