Matthews snapped the game's fifth deadlock after getting a pass from William Nylander through the crease. Once he gained possession at the left side of the crease, Matthews shoveled the puck over Christopher Gibson's stick and scored his 31st goal of the season.
Matthews' latest tally occurred after Gibson made four saves on a Toronto power play.
James Van Riemsdyk scored Toronto's fourth goal and gave the Leafs their first lead of the game 2:01 into the third by firing a shot through four defenders.
New York tied the game when John Tavares scored his 34th during a power play nearly 4 1/2 minutes later by firing into the vacated left side of the net.
Mitch Marner extended his points streak to 11 games with a goal and an assist as Toronto won for the eighth time in 10 games and completed its first season sweep of the Islanders since the 1996-97 season.
Nazem Kadri and Nikita Zaitsev also scored for Toronto.
Anthony Beuvillier, defenseman Johnny Boychuk and Brock Nelson also scored for the Islanders, who are 3-11-4 in their last 18 games.
Toronto's Frederik Andersen made 29 saves, including a point-blank stop on Tavares in the waning seconds after New York pulled Gibson for the extra attacker.
Gibson made 27 saves for the Islanders after Jaroslav Halak came down with an illness.
The Islanders took a 1-0 lead with 7:56 remaining in the first when Beauvillier lifted a shot from the low slot by Andersen's glove after getting a pass from Jordan Eberle behind the goal line. Toronto challenged the goal because it thought Eberle interfered with Anderson, but the goal stood.
Toronto tied it on the power play with 3:38 remaining when Kadri re-directed Marner's shot from the right circle over Gibson's stick side.
New York regained the lead late with 86 seconds left when Boychuk's slap shot from above the left circle went under Andersen during a power play.
Toronto forged a 2-2 tie 7:56 into the second when Zaitsev tipped in a pass from Matthews over Gibson.
Nelson made it 3-2 with 9:15 left moments after taking the ice on a delayed penalty. Nelson scored when he received a backhand pass from Andrew Ladd and lifted the puck over Andersen from the left circle.
Marner tied it for the third time when he stood with his back to Gibson and deflected Jake Gardiner's point shot into the net with 2:42 remaining in the second.
--Field Level Media
Toronto | NY Islanders | |
Nazem Kadri 2 | Points | Anthony Beauvillier 2 |
Nazem Kadri 1 | Goals | Anthony Beauvillier 1 |
Jake Gardiner 2 | Assists | Jordan Eberle 2 |
Nazem Kadri 1 | Power Play Goals | Johnny Boychuk 1 |
N/A | Short Handed Goals | N/A |
Frederik Andersen .879 | Save Percentage | Christopher Gibson .844 |
Frederik Andersen 29 | Saves | Christopher Gibson 27 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Toronto | 32 | 5 | 1-2 | 1-3 | 8 | 30 |
NY Islanders | 33 | 4 | 2-3 | 1-2 | 6 | 25 |