The results mean the cup will be won by either Malmo or Hacken for the fourth year in a row, and will see a repeat of the 2023 showpiece, which Hacken won 4-1.
2022 and 2024 winners Malmo looked to be cruising to another final when two Isaac Kiese Thelin goals in the first half put them in control at Eleda Stadion.
His first was a cool finish just after the half-hour mark, before doubling the lead with a tap-in in first-half stoppage time.
They should have been three up in the second half when Taha Ali rounded the goalkeeper, but somehow failed to roll the ball into an empty net.
That allowed Goteborg to get back into the game and with 19 minutes to go, Max Fenger nodded home after the home side failed to clear a corner.
With three minutes remaining, the comeback was completed by Kolbeinn Thordarson, who met Sebastian Clemensen's cross and planted a header into the top corner, sending the tie to extra time.
The match seemed destined for penalties until the 112th minute, when Oliver Berg steered a first-time finish into the bottom corner to send Malmo into the Final again.
The Sky Blue will again face Hacken in the Final on May 29th, after The Wasps came from behind to beat Norrkoping at home.
The visitors took the lead when David Moberg Karlsson was sent through on goal before selflessly squaring the ball to Tim Prica, who bundled it home.
From then on, Hacken were in full control, equalising six minutes later when Srdjan Hrstic finished off some neat work from Zeidane Inoussa.
The home side took the lead on the stroke of half-time when Silas Andersen's shot hit the post and was only cleared as far as Adam Lundqvist, who smashed it into the net on the half volley.
The Gothenburg club booked their tickets to the final in great style seven minutes from time, when Hrstic teed up Samuel Leach to apply the finish for 3-1.