Boston goalie Tim Thomas had to touch only one of the first six shoots in the shootout -- with two hitting posts -- before Kubina walked in and scored on a backhander. Boston's Petteri Nokelainen then got the puck past Toronto's Scott Clemmensen, but his shot hit the crossbar.
John Pohl and Chad Kilger had a goal and an assist and Nikolai Antropov two assists for Toronto (2-1-1). Phil Kessel and Bobby Allen both had a goal and an assist for the Bruins (1-1-1) in a game that included 78 penalty minutes.
The Bruins completed a comeback from a 2-0 deficit and took a 3-2 third-period lead on their third power play goal, with Nate Thompson scoring at 6:56. But the Maple Leafs came right back and tied it on a goal by Pohl just 24 seconds later.
Toronto's John Mitchell opened the scoring by beating Thomas from the slot on the power play at 9:10 of the first period. The Maple Leafs made it 2-0 nine minutes later when Kilger scored, also on the power play.
The Bruins struck twice in the second period. Kessel beat Clemmensen at 6:35 and Allen took a pass from Kessel and sent a slap shot past Clemmensen, his former Boston College teammate, at 18:27.