Brian Rolston scored twice for the Devils, who lost for the third consecutive time on the road.
Robidas scored on a power play at 14:46 of the first period and gave Dallas a 4-1 lead. His goal at 14:09 of the third period closed out the scoring at 5-3.
The Devils battled back in the second period on Rolston's second goal of the game. Travis Zajac scored at 6:31 of the third period to cut the Dallas lead to 4-3.
Marty Turco had 31 saves for Dallas. Yann Danis gave up three goals on nine shots in the first period. He was relieved by Martin Brodeur, who took the loss after giving up two goals on 17 shots over two periods.