Hellebuyck, acquired from the Winnipeg Jets on Oct. 23, became the first goalie to win his first five games with the Devils.
Timo Meier scored two goals for the Devils (13-5-0), who have won five straight games and are 9-1-0 in their past 10. Nico Hischier had a goal and an assist. Jesper Bratt and Jack Hughes each had two assists.
Anthony Stolarz made 25 saves for the Maple Leafs (8-9-2), who are 0-5-1 in their past six.
Meier, who entered Sunday with one goal this season and none in his past nine games, gave New Jersey a 1-0 lead 8:28 into the second period. After Hischier won a face-off in the left circle, Declan Chisholm sent a pass from the left point into the slot, and Meier one-timed the puck past Stolarz.
Hischier earned an assist and became the third player born in Switzerland with 500 points in the NHL, after Roman Josi (799) and Kevin Fiala (528).
Meier made it 2-0 at 12:44 when he deflected a shot by Hughes.
Hischier pushed it to 3-0 on the power play at 9:49 of the third period, banging in a Hughes rebound. Hughes has 11 points (five goals, six assists) in his past five games. Bratt has seven points (one goal, six assists) in his past five.
Brown scored an empty-net goal at 17:23 with Stolarz pulled for an extra attacker.
Maple Leafs forward Jack Roslovic (lower-body injury) was a late scratch and is day to day. Forward Colton Sissons (lower-body injury) left late in the second period and did not return.
