Spezza scored on the power play at 7:35 of the second period as Erik Karlsson found him alone in the faceoff circle and the Senators' captain caught the inside of the post for his 23rd of the season. Spezza now has 56 points in 56 career games against the Leafs.
The Senators tied a season high with their fourth straight win.
James Reimer had 36 saves, making a number of big stops to keep Toronto in the game. The Leafs capped off their season with 12 losses in their last 15 games, leaving them below the Senators in the standings.
Milan Michalek had a chance to put Ottawa up 2-0 on a breakaway in the third period, but Reimer was able to get over and make the save along the post.
Toronto had a 23-second two-man advantage midway through the period, but was unable to capitalize.
Both teams had goals nullified in the first period. At the eight-minute mark, Toronto's Tyler Bozak had a goal called off immediately due to a high stick, and on the ensuing play the Senators had a goal of their own waived off after incidental contact with the goaltender was called.
The Senators play their final game of the season Sunday night when they take on Pittsburgh.
NOTES: The Senators were without C Mika Zibanejad, who is undergoing tests for an undisclosed condition, D Jared Cowen (lower body, day-to-day) and RW Bobby Ryan (sports hernia, out for season). LW Matt Kassian was a healthy scratch. ... The Leafs were without G Jonathan Bernier (left MCL), RW Joffrey Lupul (knee surgery), Dave Bolland (lacerated ankle) and Carter Ashton (knee). D Carl Gunnarsson was a healthy scratch. D Petter Granberg made his NHL debut.