Defenseman Marc-Edouard Vlasic scored 1:28 into the game for San Jose (32-22-7), and Jones made 19 saves. San Jose lost in regulation for the third time in 30 games when it scored first (25-3-2).
"It was a tough game. You have to give them credit," Sharks coach Peter DeBoer said, according to CSN California. "They played a hard game, a really good road game."
The Sharks took a 1-0 lead when Vlasic beat Johnson for his eighth goal of the season. But San Jose was unable to add to its lead despite controlling play for most of the first 30 minutes.
"We came out with a great start but were unable to build on it," Sharks captain Joe Pavelski said, according to CSN California.
Larsson tied the game 1-1 at 13:38 of the second period when, after a Brian Gionta shot snuck though Jones, he dove and tapped it over the line for his third goal.
"We didn't sink our heads down, we didn't get down, and I think we could have against this team the way they're playing in this building," Sabres coach Dan Bylsma said, according to the AP. "We fight back and stay real patient in the game and go stride for stride with them. It showed a lot about our team."
Neither team was assessed a penalty in the game. It was the first game in Sharks history when no penalties were called, according to the Elias Sports Bureau.
San Jose has had one power play in its past two games.
"We need to find a way to get inside to score or draw penalties," DeBoer said. "We're not doing that. We're not attacking, not creating enough."
The Sharks visit the Vancouver Canucks on Sunday. The Sabres have split the first two games of their California road trip, which ends against the Los Angeles Kings on Saturday.