Dallas' lead was short lived, as the Sens responded 50 seconds later when Nick Paul's backhand from the bottom of the right faceoff circle sailed over Khudobin's shoulder to even the score at one apiece.
Khudobin entered the game riding a 10-game point streak against the Senators, having earned a point in all 10 career appearances. His record over that span was 8-0-2 and included a .935 save percentage and 2.17 goals-against average. That streak ended tonight despite making 24 saves on 27 shots.
His counterpart, Gustavsson, finished the game with 32 saves on 34 shots.
Chris Tierney scored twice with the man advantage in the second period to put an end to the Stars' perfect penalty kill.
The Stars, meanwhile, went 0-for-2 on the power play.
Joe Pavelski gave the Stars some life with a little more than five minutes to play. With the goal, Pavelski pushed his point streak against the Senators to nine straight games and gave him points in eight straight contests at Canadian Tire Centre.