Toronto outshot Tampa Bay 15-4 after the first period and 29-8 after the second.
Namestnikov cut the lead to 2-1 at 4:09 of the third period when he got to his own rebound at the top of the goal crease and put it past Murray's outstretched left pad.
"I thought our guys played really well," Keefe said. "Even in the third period, I thought we started a little bit hesitant early in the period but found our legs and just got back to playing, which is what we talked about after the second period. We were in a good spot for a good reason, let's just stay with it."
Pierre Engvall scored into an empty net with 1:46 left to make it 3-1 and Nylander scored a second empty-net goal with 32 seconds left for the 4-1 final.
"That's the same team we've played and the exact style and the exact same everything with less players," Cooper said. "It's the NHL, I get it, there's 82 games, you're not going to have your best every single night, but we started trying to manufacture things out of nothing and we were just giving them opportunities. Everything we talked about doing, I'm not sure we did at all tonight. That was a complete game, I'll tell you that, a complete bag of you-know-what, that's what that was."
NOTES: Maple Leafs defenseman Rasmus Sandin left the game at 1:01 of the second period because of a neck injury and did not return. Keefe had no further update after the game. … Maple Leafs forward Calle Jarnkrok, who played his 600th NHL game, had an assist and played 12:50 in his return after missing seven games with a groin injury. ... Bunting has 13 points (four goals, nine assists) in the past 12 games. … Matthews has 17 points (eight goals, nine assists) in the past 11 games. … Forward Mitchell Marner extended his home point streak to 13 games (four goals, 15 assists) dating to Nov. 2. He is the 10th player in Maple Leafs history with a run of at least 13. Darryl Sittler set their record of 18 in 1978. … Lightning defenseman Mikhail Sergachev played 22:48 after missing two games with an upper-body injury. … Tampa Bay forward Nikita Kucherov had his seven-game point streak end (two goals, 10 assists) and a six-game assist streak end (10 assists). … Lightning forward Steven Stamkos had an assist and has at least one point in 16 of the past 17 games (nine goals, 15 assists). … Lightning forward Brandon Hagel had a five-game point streak (five goals, four assists) and a four-game assist streak end.