Toronto had trouble putting away the Senators and found itself under pressure late after Alfredsson made it 5-3. Greening stuffed in the puck to make it 5-4 at 18:03 of the third period with Ottawa goalie Ben Bishop on the bench.
As usual, Stompin' Tom Connors' "The Hockey Song" was played midway through the third. It made for a sad interlude this time, given news during the game that the Canadian music icon had passed away at 77.
"Stompin' Tom, you'll be missed. Thanks for all the memories and the greatest hockey song ever," public address announcer Andy Frost said during the song.
Wracked by injuries, the Senators have relied on some stingy defense. They came into the game ranked second behind Chicago in goals against, giving up just 1.83 per game.
The game marked the return of Senators wings Milan Michalek (knee) and Mark Stone (broken finger), who was making his regular-season debut.
Toronto led 2-0 after the first period despite being outshot 14-10. But the Maple Leafs were more dangerous, and goalie James Reimer was up to the task when Ottawa threatened.
Reimer has won six straight.
The Maple Leafs added to the lead at 1:20 of the second after Bozak outworked a Senators player behind the net, allowing Kessel to send the puck out in front where van Riemsdyk drove it home for his 13th of the season.
Ottawa quickly replied on a delayed penalty, with Zibanejad banging home a rebound from in-close at 2:48 for his fifth goal, cutting the lead to 3-1.
Smith cut the deficit to 3-2 at 1:40 of the third period. Left alone in front of the net, he poked in a rebound of Chris Phillips' shot from the point for his first of the season.
Kessel restored a two-goal lead at 3:42 with a low wrist shot from the circle on the power play for his sixth of the season. After being shut out in the first 11 home games this season, he has scored in two straight.
Kadri made it 5-2 when Bishop failed to control his shot at 10:18. It was Kadri's 10th of the season and fifth in three games.
An unmarked Alfredsson had time to measure his shot and beat Reimer for his fifth of the season at 12:08.
"At the end of the night I thought we were very competitive here on the road and we have to continue to push ourselves to continue to be better," Ottawa coach Paul MacLean said.
NOTES: Toronto forward Matt Frattin (knee) took part in the morning skate but did not play. ... The clubs split their two previous meetings this season, with the home team winning each time. ... The Maple Leafs entered with 22 fighting majors this season, one behind NHL-leading Columbus. ... Orr's 108 penalty minutes against Ottawa are his most against any team.