"We had a 2-on-0 in Philadelphia (a 3-2 overtime loss on Dec. 1), and neither of us shot the puck. So I had to make sure I redeemed myself," said Karlsson, whose 61 points are second to Brent Burns of the San Jose Sharks among NHL defensemen. "We played a consistent game and capitalized on the things we could."
Rookies Brendan Perlini and Lawson Crouse scored for the Coyotes (23-35-8), and Smith made 28 saves.
Arizona went 0-for-4 on the power play. They had two opportunities in the third period, including 22 seconds at 5-on-3, with a chance to go ahead by two goals.
The Coyotes took a 1-0 lead at 11:30 of the second period. Jordan Martinook and Tobias Rieder chipped the puck up the ice to Perlini, who beat Condon between the pads from the left faceoff dot.
The Senators tied it 1-1 41 seconds later. Smith made the save on Fredrik Claesson off a Karlsson pass, but Pageau was waiting in front and popped the rebound over Smith to score in his third straight game.
The Coyotes took a 2-1 lead when Crouse scored with 2:11 left in the second.
Karlsson tied it 2-2 at 12:47 of the third. Smith made a nice save on Pageau, but the puck caromed right to Karlsson, who scored into a wide-open net.
"We had lots of shots and opportunities to win that game," Arizona coach Dave Tippett said. "We had chances, but we didn't capitalize. Their tying goal is on a bad break, and the overtime is one mistake you would like to have back."