"It was a good 60 minutes," Stars coach Jim Montgomery said. "The only thing that we didn't love was a couple of turnovers in the second period. Besides that, we played pretty relentless hockey, both defensively and offensively."
Radek Faksa and Joe Pavelski scored for Dallas (3-7-1), and Khudobin came within 1:13 of a shutout before Vladislav Namestnikov scored to make it 2-1.
WATCH: [All Senators vs. Stars highlights]
The Stars lost their first three home games this season (1-2-1).
"I didn't have a lot of work, to be honest; the guys played really well," Khudobin said. "But it's a tough game to play just because you don't see a lot of work. You just have to stay focused all of the time. Even if you look at the last goal, something hits you and goes in. It's tough to play, but at the same time, we got the 'W' and that's what is most important."
Anders Nilsson made 41 saves for Ottawa (1-6-1), which has lost four in a row (0-3-1).
"He's been outstanding," Senators coach D.J. Smith said of Nilsson. "He was our best player tonight, he was our best player in Vegas (a 3-2 shootout loss last Thursday). I thought we wasted his effort here tonight. In saying that, it's a real bright spot for us that he's playing the way he is. We've got to put a real effort in front of him when he's giving us an effort like that, and you're going to get yourself a win."
Faksa gave the Stars a 1-0 lead at 18:58 of the first period when he deflected Taylor Fedun's shot past Nilsson from the slot. It was Faksa's second goal of the season.