AIK was close to the SHL in the spring, but ultimately lost the hot final series against arch-rival Djurgården.
The start of this season has not gone in black and yellow, however.
After the opening win against Västerås, AIK had lost three straight matches.
Against Oskarshamn, the team fell into a 0-2 deficit.
But 55 seconds into the end of the second period, AIK both reduced and equalized through Hugo Pettersson and team captain Oscar Nord.
After a goalless third period, Alfred Barklund decided the game after just 43 seconds of overtime, following sloppy play from Oskarshamn in their own zone.
We feel that we are the team that dominates the game and presses them down the entire game. We continue to trust what we do and go all the way, says Barklund, whose team won the shots with 34-14, to TV4 Play.
Bottom team Västerås took their first win after four straight losses, on penalties, 2-1, away against Södertälje.
Newcomer Oscar Lawner, who arrived from Linköping on Tuesday, scored a goal directly and Max Karlsson scored the only goal in the penalty shootout.
Björklöven tops the table after their fifth straight win, 4-1 over Nybro. Top scorer Fredrik Forsberg scored two of the goals.
Björklöven has only lost one point, stands at 14 points, one ahead of second-placed Bik Karlskoga, who won 3-2 away against Vimmerby.
