Mikhail Grabovski, Jeff Hamilton and John Mitchell also scored for Toronto, which won for only the second time in six games.
Gerber had given up 12 goals in his last two starts and the Maple Leafs' allowed 14 in the same span.
Against New Jersey, Gerber was a wall in front of his net.
Jamie Langenbrunner scored for New Jersey, which lost for the seventh time in nine games, although this loss snapped a two-game winning streak. The Devils outshot Toronto 48-18.
Grabovski and Hamilton scored in a 1:19 span midway through the first period to stake Toronto to a 2-0 lead, and Hanson stretched the margin to 3-0 with 4:04 left in the period.
The goal by the Notre Dame product wasn't a slap shot, however.
The 23-year-old, who was playing in his third NHL game, calmly back-handed the rebound of Jason Blake's shot past Brodeur and then celebrated with teammates with a wide grin.
Hanson signed a two-year, entry-level deal with Toronto last week. The Venetia, Pa., native had 16 goals and 15 assists in 37 games with the Fighting Irish this season before turning pro.
Grabovski got the big period going for Toronto. The rookie stole Colin White's pass around the boards, worked a give-and-go with Alexei Ponikarovsky and beat Martin Brodeur from between the circles for his 20th goal.
Hamilton got his third after a Devils turnover in center ice.
Boyd Devereaux skated the puck into the Devils' end and Hamilton got his third of the season after taking a pass from Jamal Mayers in the left circle.
For most of the opening 39 minutes, Gerber stole the show. He stopped the Devils' first 34 shots, including point-blank saves on Brian Rolston and Travis Zajac late in the period, and one unbelievable stop on Brendan Shanahan on the left doorstep of the crease with New Jersey holding a 5-on-3 manpower advantage.
Langenbrunner scored with 1:07 left in the second period on the Devils' sixth power play. Devereaux tried to skate the puck out of his end instead of shooting it out and Paul Martin stole it and found Langenbrunner for his 29th goal.
Notes: Blake picked up his 400th career assist on Hanson's goal...The oops of the night went to Zajac, who skated away after the Canadian national anthem, forgetting about the "Star Spangled Banner." ... LW Brad May is scheduled to play in his 1,000th game Wednesday when the Maple Leafs play his former team, the Sabres, in Toronto. ... Toronto won the season series 3-0-1.
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