SAN JOSE, Calif. -- The Sharks needed overtime heroics from an unlikely source to beat the worst team in the league Saturday night.

Defenseman David Schlemko scored his first career overtime goal 1:18 into sudden death to give the Sharks a hard-earned 3-2 victory over Colorado at sold-out SAP Center.

"It's not the game we want to play -- back and forth like that -- we want to grind them more," Sharks forward Melker Karlsson said. "We did for some periods, but not the whole game. We got the two points, that's what's important."

Schlemko crashed the net to punch home a rebound of Logan Couture's second shot of the overtime period for only his second goal of the season. Goalie Martin Jones was excellent again, making 31 saves.

"Rebound came right to me, just had to tap it in," Schlemko said. "I'll take those any day."

San Jose won their fourth straight game and sixth in eight tries. The Sharks and the NHL's overall last-place Avalanche play again on Monday in Denver.

"I liked the way the team played," Colorado coach Jared Bednar said. "We're starting to get some traction on the way we want to play. We don't always get the results. A couple of mistakes ended up in our net."

Colorado, winners of only two of its previous 16 games coming in, tied the game 10:24 into the third period when defenseman Francois Beauchemin stepped into a one-timer from the top of the left circle to score his second goal of the season with a blast that sailed over the right blocker of Jones.

"It just came off his stick, it was a good shot," Jones said. "I didn't see it."

San Jose received a tie-breaking goal from Melker Karlsson late in the second period to take a 2-1 lead. Karlsson tipped Ryan Carpenter's drive from the right circle over the left catching glove of Colorado goalie Spencer Martin, who was making his NHL debut.

"The first few minutes were tough but after that I settled in," said Martin, who finished with 27 saves. "I thought we played them really well. It's the biggest thrill of my life so far. I'll never forget it."

Karlsson's fifth goal of the season came at 15:01, and marked a third straight game the fourth line contributed a goal.

"You can see they're playing with confidence, playing hard, and giving us a lot of energy that way," Sharks captain Joe Pavelski said of the fourth line. "And they're getting rewarded also. It's something good to see where you're getting those goals off of people in front of the net, tips and stuff. That's how you get a lot of goals."

Colorado tied the game earlier in the period by converting an odd-man break at even strength. Brent Burns gambled with a missed poke check at center, which allowed speedy Avalanche forward Nathan MacKinnon to skate around the Sharks defenseman.

MacKinnon delayed with a toe drag as San Jose defenseman Paul Martin dove to try and prevent a pass, but the puck deflected right to Mikhail Grigorenko, who poked in his fifth goal of the season at 10:30 on Colorado's 17th shot.

"We did a pretty good job in our end, but we probably played there a little too much," Schlemko said. "We didn't execute as well as we would have liked coming out of our end and through the neutral zone. But there's going to be games like that. It's good to find a way to win."

The Sharks scored the only goal of the opening period despite getting outshot 13-9.

Jones made a save 15 seconds after the opening faceoff on ex-Shark Matt Nieto's slapper from the left circle and Burns bailed out his goalie by pinning a drive on the far post that slipped through the goalie off the stick of Colorado defenseman Nikita Zadorov.

San Jose struck 1:19 into Beauchemin's high stick of Kevin Lebanc a short time later. Sharks center Joe Thornton picked up career assist No. 991 with a backhand feed to Joel Ward, who tapped in his fifth goal of the season with the power-play strike at 5:36.

"We found a way to make sure to get it to OT and we got a point," Bednar said. "That's a pretty good road game for this team. We are coming on. It can be discouraging at times when you don't get the results."

NOTES: Colorado rookie G Spencer Martin, recalled from San Antonio for the fourth time Wednesday, was named an AHL All-Star with a 15-9-2 record, 2.62 goals-against average and .915 save percentage. ... San Jose F Tomas Hertl, out since Nov. 17 with a knee injury that required a minor surgical procedure, appears close to returning after missing his 30th game Saturday. He skated hard Saturday, participated in contract drills and suggested he might return sometime next week when the Sharks are scheduled to play three games before the All-Star break. ... Avalanche starting G Semyon Varlamov missed a second straight game with a groin injury that will keep him out indefinitely. ... Colorado RW Rene Bourque and D Tyson Barrie did not play with lower-body injuries and are considered day-to-day. ... F Joe Colborne and D Patrick Weircioch suited up, leaving Colorado with no healthy scratches. ... The Avalanche continues to play without injured D Erik Johnson (broken fibula). ... Colorado F Matt Nieto played his first game against his ex-teammates. The Sharks, who selected Nieto in the second round of the 2011 draft, placed Nieto on waivers in early November. Nieto played five straight games beforeSaturday on Colorado's second line alongside LW Gabriel Landeskog and C Matt Duchene. ... RW Barclay Goodrow and D Tim Heed were healthy scratches for San Jose.