Fourth-liner Mike Brown had Toronto's other goal on a night when all of the Leafs' offense came from players who've combined for all of 13 goals -- no more than five for any player.
"If you want to make the playoffs, you need secondary scoring," Kadri said.
The win gives the Leafs 74 points, keeping them four behind eighth-place Buffalo, which has two games in hand. Toronto is 13-6-5 since the All-Star break and has matched its points total for all of last season.
"It's not over 'till it's over," said rookie goaltender James Reimer, who was back in the net after Jean-Sebastien Giguere played in Thursday's 4-0 loss at Florida and made 35 saves. "We've got to keep winning, take care of our business, and hope that other teams give us a chance and beat the teams we're trying to catch.
"It's a little bit of scoreboard-watching. All we can do is play our best and hope that's good enough for now."
The Bruins, still first in the Northeast Division despite a 1-3-3 slump, got goals from defenseman Adam McQuaid and checker Daniel Paille.
It was the first trip back to Toronto for Tomas Kaberle since he was dealt to Boston on Feb. 18. He played the first 878 games of his NHL career with the Maple Leafs -- eighth on the franchise's all-time list -- and admitted prior to the game he was experiencing "mixed feelings" about his return.
A video tribute during the first period earned Kaberle a standing ovation and he acknowledged the fans with a couple waves.
"It was really nice, from the fans," he said. "They always supported me in my 12 years here. There's lots of memories here.
"It was emotional -- there were a lot of things going through my head," Kaberle said of his return to Toronto. "We had a tough night. We have to regroup at home and make sure we get a win on Tuesday."
Said Schenn: "Kabby did a great amount for this organization, this team, and people respect him. I think you could tell that. He's missed here in Toronto, but other guys have to step up. We have a lot of young guys here that are playing in different situations because he's gone."
Schenn, not known for his offensive skills, started the scoring by going end-to-end, a la Bobby Orr (who was watching from a private box) before beating Tim Thomas with a high wrist shot at 9:44 for his fourth goal of the season.
McQuaid evened the score just over two minutes later when his shot from the corner deflected off defenseman Dion Phaneuf's skate and past Reimer.
Kadri's first NHL goal at 12:26 and had to withstand a video review. His wrist shot from the point hit McQuaid's arm and fooled Thomas.
"Not exactly how I drew it up, but it shows that if you throw pucks at the net, good things happen," said Kadri, who was picked seventh in the '09 draft. "I was fortunate to get one there."
Toronto blew the game open in the second period shortly after Reimer denied Tyler Seguin on a clear breakaway to keep his team ahead. Crabb and Brown scored 39 seconds apart to make it 4-1 and chase Thomas. Replacement Tuukka Rask was beaten by Aulie's wrister at 17:23 and showed his frustration afterwards -- then ended up watching the third period from the bench as Thomas went back out.
Paille's goal in the final half-minute made the score closer than the game.
Material from team media and wire services was used in this report.
1 - 0 TOR
1 - 1 Tie