"We fell behind, but we never quit going," Kesler said. "We really wanted this one going into a break. We've all been on the other side of this, when you lose and think about it for three days. So we're going to enjoy this one, re-energize and come back."
Cam Fowler got the tying goal with 4:16 left in regulation, and Frederik Andersen made 30 saves for the Ducks, who have won nine of 11 and own a league-best 51 points. They lead the Pacific Division by eight points over the Sharks.
Fourteen of Anaheim's last 16 victories have been decided by one goal. Two ended in overtime and three went to shootouts.
"I know this group pretty well, and I knew they were going to play today and give it their best effort," Ducks coach Bruce Boudreau said. "We played a very good hockey club and snuck away with two points."
The Ducks began overtime with 53 seconds of power-play time. San Jose killed the penalty, but Kesler beat Antti Niemi with a wrist shot from the left circle 5 seconds later.
Niemi got the Sharks to overtime with a spectacular glove save against Kesler from the top of the left circle during a power play.
"He stopped me at the far post a few times. Third time is a charm," Kesler said. "Whenever you score in that fashion, it's always exciting."
Melker Karlsson scored his first NHL goal, Joe Pavelski connected on a power play, and Niemi made 29 saves for the Sharks, who lost for the second time in 11 games but still lead the season series 2-1.
"Those guys are good, but we expect to beat them," Pavelski said. "We have a group of guys that believe in what we're doing, and they're playing the right way. We think we can play with any team.
"When Niemi's going like that, we can be aggressive and play our system knowing he's back there."
Karlsson, playing in his sixth NHL game, put the Sharks ahead 2-1 with 12:04 remaining. His slap shot from above the right circle went in off Andersen's pads as he flopped to his knees.
But Fowler tied it by scoring off a cross-ice pass by Ryan Getzlaf from the left boards.
"We continue to develop the mentality that we never give up. We'll go into this break and enjoy this win," Fowler said..
Rackell, playing in his 47th regular-season game, got his stick on a bouncing puck in front of the crease with defenseman Justin Braun in front of him and poked it past Niemi's right leg at 7:20 of the second period.
"The puck ended up on my stick in front of the net," Rakell said. "It felt good. It was a big relief for me. Christmas is saved."
Pavelski tied it at 2:00 of the third period with his 16th goal and ninth on the power play, redirecting Brent Burns' shot from the right point.
The Sharks had a couple of good scoring chances in the first period, but Patrick Marleau hit the left post at 3:08, and Tomas Hertl was robbed in the final minute when Andersen made a sprawling leg save.
The last time the Ducks hosted the Sharks on Oct. 26, the teams combined for 165 penalty minutes -- 127 in the third period. There was only one fight in the rematch.
NOTES: The Ducks had faced seven straight Canadian opponents. ... Joe Thornton's assist on Pavelski's goal was his 874th, overtaking Phil Esposito for 22nd place on the NHL list. ... The Ducks were 0 for 3 on the power play, and are just 5 for 53 against the Sharks since the start of the 2011-12 season. ... The Sharks don't play again until Saturday night at Los Angeles. ... Fowler and Ducks teammate Matt Beleskey played in their 300th regular-season game.