Matheson scored on a snap shot to push the lead to 5-1 at 18:41 of the second.
"Kind of all through this game, we were a little sloppy," Matheson said. "It's a tough way to play. Teams are really good on the transition now."
Tim Stutzle cut it to 5-2 with a wrist shot at 1:45 of the third period before a shot from Batherson went in off Norris' skate to make it 5-3 at 3:33.
Alex Formenton was awarded a penalty shot after Evan Rodrigues was called for holding at 7:27, but Jarry made a pad save.
Norris tapped in a pass from Erik Brannstrom, cutting it to 5-4 at 8:02.
"Going into the third, we knew the score was 5-1 but it really didn't feel that way," Senators defenseman Thomas Chabot said. "We played great the whole game. I think that's what we tried to do in the third. We tried to go back and stick with what we were doing. I think we have to take some pride out of that."
Jake Guentzel scored into an empty net for the 6-4 final with 47 seconds remaining.
"Not ideal," Penguins forward Bryan Rust said. "I think there were large portions of that game where we didn't play the way that we should be playing and the way we had been playing in the past. We've got to look at that and clean that up."
NOTES: Senators goalie Matt Murray, who won the Stanley Cup with the Penguins in 2016 and 2017, did not play because of an illness unrelated to COVID-19. Murray has not faced his former team since being traded to Ottawa on Oct. 7, 2020. He was in the press box and received a tribute video during the first period. … Pittsburgh defenseman Kris Letang had the secondary assist on Crosby's goal to extend his NHL career-long point streak to nine games. He has scored 14 points (two goals, 12 assists) during that stretch. … Penguins forward Jason Zucker and goalie Louis Domingue were placed on injured reserve with undisclosed injuries Thursday. Zucker scored twice in a 5-3 win against the Vegas Golden Knights on Monday, his return from missing seven games with a lower-body injury. ... Ottawa forward Nicholas Paul had three shots on goal in 13:57 of ice time during his 200th NHL game.