The Stars took the lead in the Pacific Division with their second straight win. Ottawa had won its two previous games and had captured five out of seven.
Milan Michalek put the Senators in front 2-1 with 8:18 to play in the second contest of a three-game road trip.
Dvorak tied it with 5:34 left with his third goal of the season and Nystrom produced the winning goal with 2:20 to go. Dvorak assisted on Nystrom's goal.
Craig Anderson allowed three goals on 27 shots.