Tomas Plekanec and Mike Johnson also scored for Montreal (33-26-6), which vaulted over the idle New York Islanders and Carolina Hurricanes into seventh in the Eastern Conference, although both teams hold games in hand.
Toronto went into the third period down 5-2, but Jeremy Williams, with his second goal in as many NHL games, and Alex Steen scored early in the third to wake up the boisterous Toronto contingent in the crowd of 21,273.
The Leafs were incensed when officials failed to call a high-stick on Mats Sundin by Montreal's Garth Murray with 1:31 left to play, but the non-call held up even after a huddle by the four officials.
Toronto outshot Montreal 36-24, including 14-5 in the third.
Bates Battaglia and Bryan McCabe also scored for 10th-place Toronto (30-25-9), which ended a three-game road trip. The injury-riddled Leafs lost in regulation time for only the fourth time in 15 games.
Toronto's Andrew Raycroft left the game following Souray's goal at 12:24, giving up five goals on 16 shots. Jean-Sebastien Aubin took over and stopped all eight shots he faced.
Souray's 16th power-play goal of the season left him two short of the NHL record for defencemen set in 1974-'75 by Denis Potvin and tied in 1998-'99 by Adrian Aucoin.
Souray's 22 goals is the most by an NHL defenceman since Sergei Gonchar had that number in 2001-2001.
On Tuesday night, the Leafs are at home to face Buffalo while Montreal travels to New York to play the Rangers.
Battaglia lifted John Pohl's pass over David Aebischer 4:10 into the game, but Plekanec got it back at 5:48 after some gritty work in the corner by Alex Kovalev, who returned after missing seven games with a sore elbow.
Ryder converted Koivu's pass at 14:12 for his fifth goal in five games and Johnson scored off a faceoff won by Radek Bonk at 19:10.
McCabe's long shot eluded Aebischer on a power play 1:32 into the second but Koivu answered by shooting Chris Higgins' rebound into a open side at 10:02.
A Sundin pass went off Battaglia's leg to Williams, who scored into the open side 1:02 into the third. Williams, called up Friday from Toronto's AHL club, also scored in his NHL debut last April 18 against Pittsburgh. The Regina native had two goals on his first three NHL shots.
Steen was on his off-wing when his high wrist shot beat Aebischer at 4:40 and set up a thrilling third.
Notes - Defenceman Brendan Bell didn't dress for the Leafs . . . Montreal's Sergei Samonsov didn't play, but Koivu did for Montreal. Both missed practice Sunday with the flu . . . With Steve Begin returning from a broken foot, Andrei Kostitsyn was returned to Hamilton of the AHL. Janne Niinimaa was a healthy scratch while newly acquired Josh Gorges will join the team Tuesday in New York.