Alexander Barabanov scored, and Mackenzie Blackwood made 28 saves for the Sharks (9-27-3), who haven't won since defeating the Jets 2-1 on Dec. 12 and have lost at least 10 in a row twice this season (11 from Oct. 12- Nov. 4).
"Our guys are competing their [butts] off and they keep plugging away, and they're going to show up again tomorrow and we're going to get out of this," San Jose coach David Quinn said.
Barabanov gave the Sharks a 1-0 lead at 10:26 of the second period with a wrist shot off a pass by William Eklund on the power play, but Barron tied it 1-1 at 11:48 when he deflected a shot by Neal Pionk that trickled past Blackwood.
"At the end of the day, you've got to find ways to win. It's frustrating right now," San Jose forward Luke Kunin said. "Guys are working, trying to get out of this, and the only way out is to just keep your head down and get to work."