The Sharks (44-23-10) had won eight in a row, which was tied for the third-longest streak in their history.
Aaron Dell made 29 saves for San Jose, which is five points behind the Vegas Golden Knights for first place in the Pacific Division having played one more game.
The Sharks defeated the Chicago Blackhawks 4-3 in a shootout Monday.
"I think it's our fifth game in eight nights tonight, so I was real proud of our group," San Jose coach Peter DeBoer said. "A short bench, [forward Barclay] Goodrow went down a minute in, so I think he played for a minute. So we had a lot of factors going. I thought the guys dug deep and found a way to get a valuable point."