Burns scored the tying and go-ahead goals Saturday during a four-goal third period that carried the Sharks to a 5-3 victory against the Dallas Stars at American Airlines Center.
San Jose trailed 3-1 after two periods, but got a goal by Patrick Marleau and two by Burns to take the lead before Joe Thornton's empty-netter with 41.5 seconds remaining wrapped up the victory for the Sharks in the opener of a seven-game road trip.
"As a team we talked about staying the course, staying tight, staying positive," said Burns, who is second among NHL defensemen with 15 points, including a League-high six goals. "Sometimes that's tough when things don't seem to be going your way and they get some bounces, but [goaltender Alex Stalock] hung in real tough there and played real well for us coming down the stretch and we were able to capitalize on some in the third."
Dallas finished 0-3-0 on its homestand and is 0-5-2 in its past seven games. Tyler Seguin scored all three goals for the Stars, who are 1-3-4 on home ice.
"That's a hurting group in there, but they've got a lot of try," Stars coach Lindy Ruff said. "They've got a lot of care, and they've got a lot of try. And there's a lot of frustration, a lot of emotion. I've got to be the guy that supports them."
Marleau's goal, his fifth of the season, came at 3:51 of the third with the Sharks on the power play. Joe Pavelski's close-range shot was stopped by Dallas goaltender Anders Lindback, but Marleau evaded defenseman Trevor Daley and poked the rebound into the net to make it 3-2.
"We made a mistake," Ruff said. "We won the draw on a penalty kill, and got above the puck. That hurt us. That gave them life."
Burns tied it at 6:38 when he beat Lindback with a slap shot from the left circle, capping a 2-on-1 with Logan Couture. Marleau got the secondary assist by digging the puck out of the corner and flipping it to Couture.
San Jose took its first lead of the night at 10:23 when Burns picked up the rebound of James Sheppard's shot and beat Lindback to the short side from the right circle for his sixth of the season.
"Offensively he's been dynamic for us," Sharks coach Todd McLellan said of Burns, who had 22 goals and 48 points as a forward last season. "He's been excellent and he's always had that in his game, so he's not surprising anybody in our organization. We're happy that it's coming out because it's got to make him feel real good back there from an offensive perspective and defensively his game's coming along as well. He's a real important player for us."
Couture had three assists, Marleau and Sheppard each had a goal and an assist, and Tomas Hertl had two assists for the Sharks.
"We just really wanted it," Sheppard said. "We came out hard. We just kept to the same thing and knew that if we played our game in the third that we had a chance, so we just played the whole time."
Stalock stopped 36 shots, none bigger than the pad save he made on a backhander by Colton Sceviour at the near post with 5:04 remaining in regulation.
"I thought Alex was very good," McLellan said. "He gave us a chance to come back tonight. He made some really good saves. We've been on the other side of the coin where [Ryan] Miller the other night won a game for them [the Vancouver Canucks]. Al played exceptionally well."
Seguin scored twice in the first period and once in the second for his sixth career hat trick, five of which have come with Dallas. He leads the Stars with 10 goals.
Seguin opened the scoring 8:03 into the first period when a slap shot by Sergei Gonchar from the right point hit his left shoulder and went past Stalock. He scored again at 10:26 with a wrister from the right circle that sailed under Stalock's right shoulder.
Sheppard made it 2-1 at 17:14, but Seguin completed his hat trick at 15:28 of the second period when he popped in the rebound of Jason Spezza's shot from the left circle for a power-play goal.
"I had a good stick tonight," Seguin said.
Spezza, appearing in his 700th NHL game, picked up the primary assist, the 700th point of his career. Stalock stopped his blast from the left point, but the rebound came to Seguin in the left circle and he quickly converted top shelf into the far side of the net. The goal came 10 seconds after San Jose's Tyler Kennedy was sent off for tripping Dallas defenseman Kevin Connauton.
Dallas, who last won Oct. 21 against the Vancouver Canucks, had been in an 0-for-17 power-play slump before Seguin's third goal.
This is the Stars' first seven-game slide since they went 0-5-2 from March 17-30, 2009, under then- coach Dave Tippett.
"I've never seen anything like this," Ruff said. "Frankly, I don't know how to answer."
Lindback made 24 saves but lost for the third time in as many starts this season.
"I wish I had the answer. We need to get better," Daley said. "We're not getting the job done. That's tough."