Bolland scored in overtime after Joffrey Lupul had the tying goal with 31 seconds left in regulation, leading the Maple Leafs to a 6-5 victory against the Oilers on Saturday night.
Bolland, who scored the Stanley Cup-winning goal for the Blackhawks last summer, finished off a 3-on-1 rush with Cody Franson and Jake Gardiner just over two minutes into the extra period.
"We have confidence, we just don't give up," said Bolland, who was acquired in a June trade. "In Chicago, when I was there, we'd be down 5-4 or 5-1 against teams and we knew we could come back. We have that feeling in the room. If we're down, we can come back."
"Our guys were battling hard and we couldn't keep the surge from coming," Oilers coach Dallas Eakins. "I thought we were doing a lot of great, great things and it just seemed like that puck kept coming in our net."
The Oilers and Maple Leafs scored two in the first, one in the second and two more in the third in the wild game, with neither team able to take more than a one-goal lead.
"It was back and forth, and we kept coming," Leafs captain Dion Phaneuf said. "That's probably one of the most momentum swings -- back and forth, back and forth -- that you're going to see."
Edmonton opened the scoring with a controversial goal. Bernier went behind the net to play the puck around the boards, and Eberle clipped his right foot as he tried to squeeze between Bernier and the post. Bernier tripped, Eberle got the puck out front and it deflected off Smyth's skate and over Bernier as he scrambled back into the net.
"I thought I made the right play," Bernier said. "He kinda caught me from behind, so that's why I was late on that play. But that's part of the game and that's the referee's call."
Toronto responded at 9:47 of the first. Kadri took a pass from Mason Raymond at the left faceoff dot and roofed a wrist shot over Dubynk just a few feet from the goal line.
The Leafs then took the lead on a power-play goal at 15:26 of the opening period. Van Riemsdyk tipped a wrist shot from the point by Franson past Dubynk for his fourth goal of the season.
The Oilers got that goal back on a 5-on-3 power play late in the first. With Colton Orr and van Riemsdyk in the penalty box, Nugent-Hopkins snapped a shot from the slot that snuck between Bernier's right arm and his body into the net.
Gordon had an easy tap-in in the second, and Lupul converted a one-timer off a pass from Kadri. And the roller-coaster ride then continued into the third.
The Oilers retook the lead at 5:29. Franson got trapped at Edmonton's blue line, leaving Morgan Rielly to defend against Arcobello and Eberle on a 2-on-1 break. Arcobello passed to Eberle, who snuck a shot over Bernier's left shoulder for his first goal of the season.
It took less than five minutes for the Leafs to tie the game again, with van Riemsdyk catching Dubnyk leaning the other way on a wraparound.
"My teeth are going to be ground down by the 20-game mark if we keep playing the way we did tonight, as far as exchanging chances and mistakes," Maple Leafs coach Randy Carlyle said. "But hey, that's hockey and it's early in the season."
Edmonton's Nail Yakupov, who has no points in four games, was a healthy scratch for the first time in his career. Yakupov was the No. 1 overall selection in the 2012 NHL draft. ... The Oilers have given up at least four goals in every game this season.
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