Kyle Wellwood tied the game earlier in the period, and Vesa Toskala got the win by stopping 27 shots.
With a chance to clinch the game, Darcy Tucker's goal was disallowed with 4:04 left as linemate and former Islander Jason Blake was called for goaltender interference.
Alexei Ponikarovsky clinched the game with an empty-netter with 27.7 seconds left.
Rob Davison scored the only goal for the Islanders over their past two games. New York has lost six in a row overall, and five straight at home. Dubielewicz stopped 23 shots.
The Islanders, with 177, have the fewest goals in the NHL. Only Bill Guerin and Mike Comrie have surpassed the 20-goal mark for the team.
Dubielewicz got the start because Rick DiPietro had an MRI on his hip earlier in the day. He first injured the hip during the skills competition at the All-Star game.
Toronto had a chance to grab an early lead, but defenseman Bryan Berard blocked a shot off the stick of Carlo Colaiacovo just over three minutes in.
The Islanders took the lead on one of the longest goals of the NHL season at 13:48. Killing a penalty, Davison tried to clear the puck from his goal line. The puck was bouncing all the way, and as Toskala went to glove the puck, it took a sharp, high bounce over his glove and ended up in the net.
The goal was Davison's first of the season and third in his career.
Toronto had the first seven shots of the second period, and nine of the first 10, but Dubielewicz was sharp. His best save came at 7:48 as he got his right pad against the left post to stop Matthew Stajan's stuff attempt on a short-handed breakaway.
Toronto tied the game at 7:24 of the final period when Wellwood, in the low slot, tipped Alexander Steen's shot between Dubielewicz's legs.
