Drake Batherson scored to extend his point streak to seven games (six goals, six assists) and Ridly Greig also had a goal for the Senators (9-5-1), who had lost two straight and are 1-1-1 on a five-game road trip. Samuel Ersson made 21 saves for his first victory with Ottawa, and Jake Sanderson had two assists.
Michael Misa scored for the Sharks (7-7-1), who have lost three of their past four games. Alex Nedeljkovic made 30 saves.
Batherson put the Senators ahead 2-1 at 5:04 of the second period. He scored on the rush with a wrist shot from the inside edge of right face-off circle after taking Philip Tomasino’s return pass from the right point.
Stutzle extended the lead to 3-1 at 10:54. Sanderson took a drop pass from Cozens at the top of the right circle and found Stutzle on the left wing, where his wrist shot beat Nedeljkovic over the blocker.
Greig made it 4-1 with a short-handed goal at 12:17. Pinto found Greig skating down the middle on a 2-on-1, and Greig made a move to the backhand to beat Nedeljkovic by his left pad.
Pinto added an empty-net goal at 17:30 of the third period for the 5-1 final.
Cozens had put the Senators up 1-0 at 13:25 of the first period. Cozens raced down the right wing around San Jose defenseman Darnell Nurse and put a snap shot through Nedeljkovic's five-hole.
Misa tied it 1-1 at 16:06. Jacob Trouba had his shot from low in the right circle stopped by Ersson before collecting his own rebound and feeding Misa at the edge of the crease, where he finished into an open net.