Kesler's second goal capped a stretch in which the teams combined to score three goals in 37 seconds.
Carolina's Cam Ward made 27 saves.
The Hurricanes, who failed on six power-play chances against the NHL's best penalty-killing unit, have lost six of eight.
RED WINGS 4, SENATORS 2
OTTAWA, Ontario (AP) — Daniel Alfredsson scored an empty-net goal and added an assist in his return to Ottawa, and Detroit beat the host Senators.
Alfredsson, the former longtime captain of the Senators, wasn't primarily responsible for Ottawa's second straight loss and fourth consecutive at home, but he helped contribute to the continuation of his ex-team's woes.
Like so many times in their previous 27 games in the post-Alfredsson era, something was missing for the Senators (10-13-4). Defensive breakdowns led to goals, and there wasn't enough offence to compensate.
The Red Wings, who won their fourth straight, haven't lost since the Senators beat them on Nov. 23.
OILERS 3, STARS 2, SO
Dubnyk stopped two of three shots in the tiebreaker. Dallas' Kari Lehtonen failed to make a save in the shootout.
Ryan Garbutt scored two goals, including a short-handed tally that gave Dallas a 1-0 lead in the second period. He also put the Stars ahead in the third.
Garbutt nearly had a hat trick but he was stopped on a breakaway attempt by Bryzgalov with 3:41 left in the second. Garbutt collided with Bryzgalov, who left with an upper-body injury and didn't return.
Bryzgalov, who made 28 saves, trailed 1-0 when he came out.