Stutzle gave Ottawa a 3-2 lead at 13:22. He skated in on a 2-on-0 with Nick Cousins, and San Jose goalie Alex Nedeljkovic stopped Cousins’ backhand with his outstretched left pad before Stutzle poked the puck off the goal line and into an open net.
Dylan Cozens and Fabian Zetterlund also scored for the Senators (11-6-4), who have won the first two of a seven-game road trip and are 5-1-1 in their past seven. Linus Ullmark made 17 saves.
John Klingberg and Barclay Goodrow scored, and Nedeljkovic made 24 saves for the Sharks (10-9-3), who had won two in a row. Macklin Celebrini had an assist to extend his point streak to four games (six points; three goals, three assists).
Will Smith appeared to give the Sharks a 1-0 lead 1:27 into the first period but his goal was overturned after the Senators challenged for offside.
Cozens put Ottawa in front 1-0 at 7:50 with a power-play goal. Stutzle skated down the left wing and threw a pass to the slot that Cozens redirected past Nedeljkovic's left pad.
Klingberg tied it 1-1 on the power play at 16:04. After taking a pass from Celebrini, Klingberg scored with a wrist shot from above the right circle that went over Ullmark's blocker.
Goodrow made it 2-1 for San Jose at 7:47 of the second period. After Ullmark stopped Mario Ferraro’s one-timer on the rush, Alexander Wennberg backhanded a rebound and scored off Goodrow’s skate.
Zetterlund then tied it 2-2 at 18:38. Tyler Kleven found him cutting through center ice, and Zetterlund’s wrist shot from the right circle beat Nedeljkovic over the glove.
