DeBoer was hired Sunday to replace Patrick Roy.
Calum Ritchie had a goal and an assist, and Tony DeAngelo had two assists for the Islanders (43-31-5), who ended a four-game losing streak. Ilya Sorokin made 13 saves.
Steven Lorentz, Easton Cowan and Morgan Rielly scored for the Maple Leafs (32-33-14), who have lost four straight. Artur Akhtyamov made 39 saves in his first NHL start.
Brayden Schenn gave the Islanders a 1-0 lead at 2:08 of the first period. On a delayed penalty, Bo Horvat dove in the slot to get the puck to Ritchie, who found Schenn at the top of the crease for the finish into an open net.
Jean-Gabriel Pageau extended the lead to 2-0 at 4:55. He poked in the puck behind Akhtyamov after the goalie stopped his initial attempt at the right post.
Lorentz cut it to 2-1 at 5:11, beating Sorokin with a wrist shot from the left circle that got inside the left post.
Cowan tied it 2-2 on the power play at 1:57 of the second period. He scored with a wrist shot from the top of the slot with Sorokin screened.
Matthew Schaefer then gave New York a 3-2 lead at 9:39 when he put a wrist shot through the five-hole from the left circle. With his 23rd goal of the season, Schaefer tied Brian Leetch (1988-89) for the most goals in a season by a rookie defenseman in NHL history.
Emil Heineman’s power-play goal extended the lead to 4-2 at 16:44. Mathew Barzal found him at the top of the slot with a short feed, and Heineman beat Akhtyamov glove side.
Ritchie pushed it to 5-2 during a 5-on-3 man-advantage at 10:19 of the third period when he banged in a loose puck at the side of the net.
Rielly’s pass to the crease deflected off Barzal’s stick and through Sorokin’s legs at 14:04 to cut the Maple Leafs deficit to 5-3.
