Marner, who has 26 points (nine goals, 17 assists) during the streak, broke the record he shared with Darryl Sittler (1977-78) and Eddie Olczyk (1989-90).
"It's cool. I grew up in this city, I love being a part of this team nowadays," Marner said. "It's special to me and it's special growing up to watch this team play hockey, and now to have my name on something pretty amazing, it's hard to describe, but like I've been saying, it's not a one-man effort out there."
Alex Killorn won it with a shot from the right face-off dot 33 seconds into overtime.
"It was really tough," Killorn said. "Going into the third, 5-on-5, I personally didn't have a ton of shifts. A lot of guys hadn't got a lot of chemistry with their lines just because we hadn't had a lot of 5-on-5 play, but in the third it kind of came alive."