The defenceman lifted the Leafs into a 1-1 tie at 8:35, just 2:51 after Jaromir Jagr gave the Rangers the lead. Until then, New York held the advantage on the scoreboard and shot clock with a 20-7 edge.
The Rangers entered as the lowest-scoring NHL team (15 goals), but on the strength of goalie Henrik Lundqvist, had allowed a league-low 17.
Kubina's shot from the right point struck something and changed direction on Lundqvist 29 seconds after the Toronto defenceman left the penalty box. It was the first even-strength goal yielded by the Rangers in 230 minutes, 37 seconds, dating to an Oct. 18 loss at Atlanta.
After giving up only two regulation goals in three games, including a pair of shutouts for Lundqvist, the Rangers surrendered two to the Leafs 1:20 apart.
Toronto, which entered with the most goals in the NHL (42) and most allowed (44), grabbed a 2-1 edge on John Pohl's first with 4:14 left. Nik Antropov pushed the lead to two goals, sweeping a shot past Lundqvist as he stood untouched in front.
Chad Kilger added an empty-netter with 15.8 seconds left.
Despite being strong defensively and thwarting both power plays to give them 44 kills in 50 chances this season, New York has only three wins in 10 games (3-6-1). The Rangers snapped a four-game losing streak Thursday with a 2-0 win over New Jersey.
The offence, which generated 33 shots Saturday, has been mostly to blame.
Jagr was the only one to get a puck by Vesa Toskala, who earned his fourth win in eight games since joining the Leafs in an off-season trade with San Jose.
Taking a crafty bank pass of the right wing boards from Michal Rozsival, Jagr carried into the right circle and used six-foot-seven defenceman Hal Gill to set a screen. Jagr reached out and whipped a shot past Toskala at 5:44 for his second of the season.
Less than 12 minutes later, the Maple Leafs had turned a one-goal deficit into a two-goal lead - scoring three times in the period on only 12 shots.
Lundqvist had himself to blame on the go-ahead goal after he turned over the puck to Boyd Devereaux as he played a wraparound behind the net. Devereaux found Pohl in the slot for a quick shot.
Leafs defenceman Tomas Kaberle earned his second assist when he spotted the unmarked Antropov at 17:06.
Notes: Maple Leafs D Bryan McCabe, who played all 82 games last season, missed his second straight (groin). ... New York outshot Toronto 11-5 in the first period and held the Maple Leafs without a shot for 16:05 until Devereaux's short-handed breakaway shortly before Kubina's goal. ... Lundqvist's shutout streak was snapped at 127:33. ... Toronto got its first two shots of the third with under four minutes left.