Visnovsky's winner came after Anders Lee scored two tying goals for the Islanders in a see-saw third period in which the teams combined for five goals in a nine-minute span. Evgeni Nabokov made 18 saves for New York, which improved to 5-1-2 in their last eight games against Toronto.
Joffrey Lupul put Toronto ahead 4-3 with just over six minutes left in the third before Lee knotted the score at 17:20 with his second of the game. Lupul's 18th of the season at 13:54 came just over a minute after Lee tied it at 3 with his first of the season.
Lee's power-play goal came after Dion Phaneuf had put Toronto ahead 3-2 at 11:26.
Phaneuf's sixth goal of the season came less than three minutes after Paul Ranger tied it at 2.
The Islanders held that lead entering the third before the outburst by both teams.
Kessel opened the scoring with his 32nd of the season. Kessel, who scored five goals for gold medal-winning Team Canada in Sochi, took a pass in the high slot before whipping the puck past Nabokov. Only Washington's Alex Ovechkin has more goals than Kessel.
Grabner answered for the Islanders with his first short-handed score at 15:53 with an assist to Casey Cizikas. The Austrian forward then took advantage of a misplay by Leafs goaltender Jonathan Bernier, intercepting an attempted pass by the netminder in the crease and sliding the puck into the empty net at 16:41.
The goal was the 11th of the season for Grabner, who tied Kessel in goals at the Olympics despite playing two fewer games.
The last Islander to score two short-handed goals on the same power play was Ziggy Palffy, 53 seconds apart on April 17, 1999.
The Islanders (23-30-8), had lost seven of eight games heading into the Olympic stoppage, and were without captain and leading scorer John Tavares, who sustained a season-ending knee injury in Sochi.
New York was also minus forwards Frans Nielsen (hand) and Matt Martin (lower body). Both had played all 60 previous games this season, while Tavares had missed only one contest. The Islanders earlier this week recalled the entire top line from AHL Bridgeport: Lee, Ryan Strome and Mike Halmo, who made his NHL debut.
Nielsen, who has a career-best 18 goals, ended his streak of 189 consecutive regular-season games played.
He suffered a hand injury in New York's last game before the break on Feb. 8. Martin had played 121 straight games and also was hurt in the Feb. 8 home loss to the Colorado Avalanche.
The Maple Leafs (32-22-7) came in 11-2-1 before the break. Toronto is battling Montreal and Tampa Bay in the closely packed Atlantic Division as the Leafs trying to reach the playoffs for the second straight season after missing every year since 2004.
The Leafs had won three straight and four of their last five at Nassau. But Nabokov was strong throughout, stopping Troy Bodie with his glove four minutes into the second and denying James Van Riemsdyk — who had three assists — in front midway through the middle period.
NOTES: The Islanders are just 9-14-8 at home this season. They had lost six straight at Nassau Coliseum, including the last two before the break against Calgary and Colorado. ... It was the third and final meeting between the teams this season and the only contest at Nassau Coliseum. The teams split two games at the Air Canada Centre. ... The Islanders are 20-7-3 when they score at least three goals and are 3-23-5 when they do not.