Shane Pinto's chip shot bounced off Tierney's chest for a power-play goal to make it 2-1 at 9:20 of the second period.
Tierney scored again on the power play when he redirected a cross-crease pass from Zach Sanford at 19:00 to give the Senators a 3-1 lead.
"The penalty kill, up until tonight, has been very good," Dallas coach Rick Bowness said. "You live with that first goal; it was fluky. It hits his skate, hits the body, goes in. There's nothing you can do about that. I didn't like the second one. The defenseman's netfront responsibility is to stop that pass."
Joe Pavelski scored from the edge of the crease at 14:17 of the third period for the 3-2 final.
"We've got some guys trying to find their game, guys frustrated with their game," Bowness said. "And we're going to just kind of have to play our way through it."
Smith expressed relief that the Senators won for the second time in three games this season; they needed 11 to get their second victory in 2020-21 (2-8-1).
"To get two wins in three games is good for us, especially going into a three-day break here," Smith said. "That day off and a couple of practices, it gives us some confidence. We're playing well at home. We're going to have to continue that."
NOTES:Smith confirmed that forward Brady Tkachuk, who signed a seven-year, $57.5 million contract Oct. 14 after missing training camp, will make his season debut Thursday against the San Jose Sharks. … Stars defenseman John Klingberg missed his second straight game because of a lower-body injury. … It was Khudobin's first regulation loss against the Senators (8-1-2). … Brown got his 100th NHL assist on Tierney's second goal. … It was Smith's 50th NHL win.