Dundas found the net for visitors Sutton in the 32nd minute after racing clear from a throw-in to slide the ball past Scott Davies from 20 yards.
Tranmere, who recorded their first league win of the season with a 3-1 victory over Woking on Tuesday, came close early in the second half when Andy Cook hit the underside of the bar from Liam Ridehalgh's cross.
Sutton almost added a second in the 67th minute when Kenny Davis' shot was blocked and Craig Eastmond was also denied with the follow-up.
Report supplied by the Press Association.
Match ends, Tranmere Rovers 0, Sutton United 1.
Second Half ends, Tranmere Rovers 0, Sutton United 1.
Substitution, Sutton United. Daniel Spence replaces Ross Lafayette.
Substitution, Sutton United. Kieron Cadogan replaces Craig Dundas.
Substitution, Tranmere Rovers. Andy Mangan replaces Jay Harris.
Craig Eastmond (Sutton United) is shown the yellow card.
Andy Cook (Tranmere Rovers) is shown the yellow card.
Dean Beckwith (Sutton United) is shown the yellow card.
Kenny Davis (Sutton United) is shown the yellow card.
Second Half begins Tranmere Rovers 0, Sutton United 1.
Substitution, Tranmere Rovers. James Alabi replaces Jack Dunn.
First Half ends, Tranmere Rovers 0, Sutton United 1.
Goal!  Tranmere Rovers 0, Sutton United 1. Craig Dundas (Sutton United).
Nicky Bailey (Sutton United) is shown the yellow card.
Aswad Thomas (Sutton United) is shown the yellow card.
First Half begins.
Lineups are announced and players are warming up.
Craig Dundas scored the only goal as Sutton climbed to fourth in the fledgling National League standings with victory over Tranmere.