Sharks center Michal Handzus scored the only goal in the shootout, beating Ducks goaltender Jonas Hiller in the first round. Sharks goaltender Antti Niemi went 3-for-3 in the competition, as Bobby Ryan, Corey Perry and Teemu Selanne all failed to find the back of the net.
Trailing 2-1 entering the third period, the Sharks pulled even at 17:15 on Logan Couture's fourth goal of the season. Scott Gomez dropped a pass behind him to Couture, who rifled a shot from the right circle through the legs of Hiller and into the net.
"(Ryane Clowe) I think got the puck on the left boards, went cross-ice to (Gomez)," Couture said. "He cut to the middle and dropped it to me. He knew I was coming late. He's a playmaker, and he made a play. Just threw it at the net. We didn't shoot the puck enough tonight on net."
Joe Pavelski also scored for the Sharks, who improved to 6-0-0 despite being outshot 30-18. Niemi made 28 saves.
"We got to be excited that we put points in the bank and we were able to come back, but we have to tell it like it was," Sharks coach Todd McLellan said. "They were the better team. Didn't feel real good tonight with the flow of the game, with the management of players. Opportunities to execute, but we didn't do it. It was a frustrating night, but at least we found a way to win."
Handzus entered the game with a career shootout percentage of 50 percent, connecting 16 times in 32 attempts with seven game-deciders. He enhanced his reputation as the Sharks' go-to guy on the shootout.
"It's fun," Handzus said. "You want to be there. You want to try to help the team, obviously. It's fun. I love to go out there and score goals. I don't know what it's about. I got a couple moves. I always try to look at the goalie and pick one."
Facing Hiller, Handzus knew which move he had to make.
"He was pretty deep in the net, so I knew I had to shoot it high for sure," Handzus said. "He's a great goalie to cover the low part of the net. I thought my only chance was to just get it up, and it went in."
Niemi did the rest, with a little help from the crossbar on Selanne's shot.
"I felt pretty good all through my career in shootouts," said Niemi, who improved to 18-11 in shootouts.
Patrick Marleau's five-game streak of games with a goal came to an end, but he had an assist.
"I can't say anything negative," Ducks coach Bruce Boudreau said. "It might not happen on any other night, but I thought we outplayed them and outworked them. It's disappointing because we played so hard. When you hold this team to nine shots after two periods in this building, you're playing great."
The Sharks nearly ended things early in overtime when Marleau went on a rush and fired a shot from the slot, but Hiller made a glove save. Moments later, Joe Thornton unleashed a shot from close range, but it went just left of the post.
With just under two minutes left, Perry had a great scoring chance from right of the crease, but he misfired.
The Sharks were outshot 13-4 in the first period but owned a 1-0 lead at the first intermission. Pavelski scored his third goal of the season at 9:46 of the first as the Sharks top line delivered yet again and San Jose scored first for the fifth straight game.
Marleau got the puck in the Sharks' zone and Thornton, streaking the other way along the left boards. Thornton zipped a cross-ice pass to a wide-open Pavelski, who ripped a shot inside the right post past Hiller.
Thornton, Marleau and Pavelski entered the game with a combined 36 points and added to their impressive totals.
Niemi, who gave up just one goal Sunday against Vancouver, stopped everything that came his way in the first period and helped kill the Sharks' only penalty.
The Ducks struck twice in a span of 59 seconds midway through the second period to take a 2-1 lead on goals by Beauchemin and Beleskey.
Beauchemin scored shortly after Couture nearly scored a shorthanded goal on a breakaway. Hiller won that battle, but it appeared as if Ducks defenseman Sheldon Souray might have gotten away with a hook from behind that disrupted Couture's timing.
After Couture missed, the Ducks stormed the other way, and Beauchemin ripped a sharp-angled shot from along the left boards that bounced off of Niemi and into the net at 8:40 of the second. Saku Koivu and Ryan earned the assists.
Beleskey made it 2-1 at 9:39, taking a pass in the low slot from Getzlaf and firing a rocket past Niemi. Former Shark Daniel Winnik, who earned an assist, made it all possible when he won a battle for the puck along the boards and got it to Getzlaf.
"I think we played well," Beleskey said. "We played a good road game. It was just a game where a puck hits the ref and they go down and score and in the shootout we hit a post. If we play that way every night we're going to be a pretty successful team."
The Sharks had 12 power play goals in their first five games, but they didn't go on a power play Tuesday until 17:15 of the second period, and the Ducks killed that attempt.
At the end of the second, Anaheim owned a 21-10 edge in shots.
The Sharks were without veteran defenseman Dan Boyle, who, according to the team, missed the game with the flu. Although Boyle missed the morning skate, McLellan said then that he fully expected him to play. Boyle also missed the third period Sunday against Vancouver with what McLellan described as a nose bleed that trainers had trouble stopping.
Sharks rookie defenseman Nick Petrecki, a first-round pick in the 2007 NHL Draft, replaced Boyle and made his NHL debut.
Ducks forward Emerson Etem, a first-round draft pick in 2010, also made his NHL debut, skating on the fourth line.