John Mitchell scored twice in the Maple Leafs' outburst.
The Rangers led 2-0 when Mitchell started the comeback by scoring his first NHL goal at 12:36. Jason Blake tied it at 14:02 and Kubina notched the go-ahead goal just 52 seconds later.
Dominic Moore added a goal for the Maple Leafs (5-3-3), who have erased two-goal deficits and pulled out wins in three of their past six games.
Ryan Callahan and Blair Betts had the Rangers' goals.
New York weathered a strong start by the Maple Leafs and killed off three penalties before Callahan got them on the board.
He netted his fourth of the season with 9.3 seconds left in the first period after taking a beautiful cross-ice pass from defenseman Dan Girardi and beating goalie Vesa Toskala high with a wrist shot.
Toronto had good chances to tie it in the second period but Tomas Kaberle's point shot rang off a post. Valiquette also got his glove on a hard attempt from Alex Steen.
Betts matched last season's output with his second goal of this campaign, scored at 15:25 of the second period. Dmitri Kalinin's point shot caromed off the boards behind the goal before Betts tucked the puck in the open side.
It was the fifth time in six games that Toronto fell behind by two goals.
Notes: D Anton Stralman was back in the Leafs lineup, but Jonas Frogren, Carlo Colaiacovo and Ian White were scratched. ... Valiquette beat the Leafs 1-0 in a shootout on Oct. 17 ... Toronto forward Jason Blake played his 600th NHL game. ... Maple Leafs rookie D Luke Schenn will turn 19 on Sunday. ... Heading into the night, the Leafs had the fourth-most blocked shots of any NHL team with 162.
