The Lightning (61-16-4) are one win from matching the 1995-96 Detroit Red Wings for the most wins in NHL history (62-13-7). Tampa Bay plays its regular-season finale at the Boston Bruins on Saturday.
"We're not really talking about those records much, but it's a sign that we're consistent with our game, which we obviously want to be," Lightning defenseman Ryan McDonagh said. "We take a lot of pride in being competitive and not allowing losses to snowball into something bigger, so it's good we can have a quick response after losses this year and get back on the winning page."
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Mitchell Marner scored, and Frederik Andersen made 26 saves for the Maple Leafs (46-28-7), who will finish third in the Atlantic Division, behind the Lightning and Bruins.
"I thought we played well," Marner said. "We didn't make many mistakes, but again, we have to stop making any mistakes because people are scoring on them. We have to clean some things up, but I thought our team played well together tonight."
Steven Stamkos had a goal and an assist, and Andrei Vasilevskiy made 29 saves for the Lightning.
"We just controlled the puck and made smarter plays," Stamkos said. "I thought the other night (a 4-2 loss to the Montreal Canadiens on Tuesday), we looked a step behind -- granted we were on a back-to-back there -- but I just didn't think we had our legs. Tonight we managed the puck and supported each other a lot better, and you can tell. When we have the puck more, that's where our team is dangerous."
Killorn one-timed a pass from Stamkos in the slot at 14:12 of the third period to put Tampa Bay ahead 2-1.