Gaudette gave the Senators a 1-0 lead at 4:35 of the first period. Stuzle skated around a sliding Jake Walman on a 2-on-1 rush and sent a centering pass to Gaudette, who tapped it inside the right post.
Josh Norris made it 2-0 at 13:56, burying a one-timer over the blocker of Blackwood for a power-play goal. Stutzle started the play by winning a battle for the puck along the left boards and passing to Drake Batherson, who found Norris at the right hash marks.
Mario Ferraro made it 2-1 at 9:19 of the second period, scoring into an open net from the left circle to finish off a passing play through the slot by Smith and Klim Kostin.
Kleven, who was playing in his 39th NHL game, pushed it to 3-1 at 15:22 with a slap shot from the top of the left circle that beat a screened Blackwood.
“I just buried my head and tried to shoot as hard as I can,” Kleven said.