Winless in Pyeongchang before Tuesday, Norway erased a one-goal deficit in the third period to force the sudden-death period and went on to register their first Olympic hockey win since they hosted the Games in 1994.
They beat a Slovenian team that had played three of its four Olympic games into overtime but were also playing without one of their key forwards, Ziga Jeglic, who was slapped with a doping suspension right before the game.
The win means the Norwegians, the tournament's second-lowest scoring team with just two goals heading into the match against Slovenia, face a fearsome Russian team, the Games' highest scorers, in the quarter-finals on Wednesday.
Bonsaksen's goal, about three minutes into overtime, came after a wild sequence with a pile of players fighting for the puck in front of a sprawled Slovenian goaltender Gasper Kroselj, who had just stopped a point-blank shot.
The puck popped out to Bonsaksen near the blue line, and he took a couple of strides in and then drilled the puck through the traffic in front of Kroselj and into the net.
"I just wanted to get it past the first guy trying to block it and luckily it went in," Bonsaksen said.
Asked about the significance of the game, he said: "It's all the way up there. We talked about it before the third period. We were down one goal and let's be historic here, I mean the first time Norway's in the quarter-final, and it's been 24 years since we won a game in the Olympics."
Norway last notched an Olympic ice hockey victory at their own games in Lillehammer in 1994, beating Austria 3-1 in the final consolation game to avoid the wooden spoon.
Slovenia, which has had three of its four Olympic games go into overtime, was the first on the board, with Jan Urbas scoring on a first-period powerplay on an assist from captain Jan Mursak while Norway's Ludvig Hoff was off for hooking.
The lead lasted into the third period, when Norway, winless in three group-stage games, levelled it. Martin Roymark sent a pass across the goal crease and Tommy Kristiansen tapped it past Kroselj.
"I got a great pass, and I see the goalie was going home to the post and I tried to get it in the other side and it was going in so it was really nice," Kristiansen said.
Before his goal, Norway had scored only twice in the tournament, and heading into the game were the second-lowest scoring team after South Korea, who have just one.
The game started right after the Court of Arbitration for Sport announced Slovenian forward Ziga Jeglic had tested positive for a banned substance and would be suspended for the rest of the Games.
Jeglic had netted the game-winning shootout goal for Slovenia in their final group-stage game against Slovakia on Saturday and was a major presence on the ice for the Slovenians. Several of his team mates said after the game they did not know what was behind his sudden absence.
In a statement issued by the Slovenian's Olympic committee, Jeglic said he had been taking an asthma medication that contained the banned substance Fenoterol and he had neglected to declare it and seek an exception.
Asked if the loss of Jeglic had affected his team, Slovenia coach Kari Savolainen said: "Of course, of course. Still I'm proud of the team. They showed great energy on the ice."
(Reporting By Dan Burns; Editing by Amlan Chakraborty)
