"It's not about going back to practice [Wednesday] and change my strategy," Gustavsson said. "It's about maybe paying attention -- some extra focus in those situations."
Petr Sykora had a goal and an assist for New Jersey (34-20-4), and David Clarkson and former Maple Leafs forward Alexei Ponikarovsky also scored. Martin Brodeur made 29 saves as the Devils won their fourth in a row.
Phil Kessel's31st goal of the season forced overtime for Toronto (29-24-6) with 44 seconds left in the third period.
After Brodeur stopped Tyler Bozak's rush up the left side, Kessel banged in the rebound to send the home crowd into a frenzy.
Fayne's shot from the point at 1:18 of overtime went off the inside of Gustavsson's arm and caromed over the goal line.
"Right now we're just trying to get our game together," Brodeur said. "Even though we're winning I know we have a lot of room for improvement."
Gustavsson, who has been sharing goaltending duties with James Reimer as the Leafs have looked for a bona fide No. 1 netminder, was shaky early as the Leafs fell behind 2-0 in the first period. He rebounded to finish with 28 saves before the rough finish.
"As a group we've got to take it as a real big positive to get that point," Leafs captain Dion Phaneuf said. "It's not the way we wanted it to end, but to get that point at that point of the game, it's huge.
"It's a big goal by [Kessel] for our team, and that's the way we're going to take it. We're going to take the point and move forward."
The Devils got on the board soon after Phaneuf got out of the penalty box after a tripping penalty midway through the first period.
Standing behind the net, Adam Henrique found Sykora with a backhanded pass. Some poor checking by the Maple Leafs gave Sykora the time to get two cracks at the puck. Gustavsson couldn't hold on to the initial shot, and Sykora went around the helpless goalie and backhanded in his 14th goal of the season at 9:44.
The Devils doubled the lead when Clarkson fended off Matthew Lombardi on the right side, crossed into the Maple Leafs' zone, and put a low shot past Gustavsson at 14:16.
"The first goal he had no chance on," Maple Leafs coach Ron Wilson said. "The second one -- it's a 1-on-2 and you can see the shot from a bad angle that finds its way in. We've just got to do, I guess, a better job of supporting our goaltender."
Just 32 seconds after the Devils' second goal, the Maple Leafs got one back. Standing in front of the Devils net, Connolly reached out with his stick to deflect Cody Franson's shot from the point past Brodeur.
Good forechecking helped Toronto get even with just over five minutes remaining in the second. Mikhail Grabovski stopped an attempted Devils clearance at the blue line, and found Nikolai Kulemin, who passed to MacArthur in front for his 18th of the season.
Ponikarovsky gave the Devils a 3-2 lead with under two minutes remaining in the second.
Gustavsson redeemed himself early in the third when he made a great save against Ilya Kovalchuk, who got free after Phaneuf fell at the Maple Leafs' blue line.