Tavares tied it 1-1 with a power-play goal 1:32 into the third period. He finished a backdoor pass from Nylander at the left post.
After Pettersson and Miller gave Vancouver the lead, Aman made it 4-1 by tapping in a backdoor pass from Boeser at 12:34.
"Poor execution and elite forwards on the other side that capitalized," Keefe said. "You come out in the third period and your power play scores a huge goal and gets you in the game and then lets you down the next time out, so you're torn on that one. … So in that case, their best players were better than ours."
Toronto dressed 11 forwards and seven defensemen for the second straight game and played for a bit without forward Auston Matthews, who briefly left after taking a slap shot off the inside of his right knee with 1:18 remaining in the first period.
"I felt like I was in a lot of pain there for quite a little bit of time and just let it kind of calm down a little bit and was able to get back out there," Matthews said. "I tried to grind my way through it. It didn't feel too great but felt fine to play."
The Maple Leafs also lost forward Ryan O'Reilly after he was hit in the hand by a Matthews shot late in the second period.
"Obviously, he was unable to return, so serious enough that that was the case, but in terms of a timeline for him we'll have an update Monday," Keefe said.
NOTES: Maple Leafs defenseman Timothy Liljegren practiced on Friday but missed his second straight game after being "a little shaken up," according to Keefe, against the Edmonton Oilers on Wednesday. … Hughes became the fastest defenseman in NHL history to record 200 assists, reaching the milestone in 263 games, one fewer than Brian Leetch.