Hibernian booked a CIS Insurance Cup final meeting with Livingston after a nervous penalty shoot-out at Hampden.
Stephen Dobbie celebrates his second half goal
Rangers defender Frank de Boer missed a sudden-death spot-kick after three players from each side had also failed to score from 12 yards.
Michael Mols had given Rangers a first- half lead after Daniel Andersson saved a Mikel Arteta penalty.
But Hibs battled back to level the game with former Rangers man Stephen Dobbie netting after 79 minutes.
The match started at a fast pace, and Mols blasted a great chance over the crossbar after just 90 seconds, following a neat cut-back from Maurice Ross.
With the rain lashing down, players were slipping and sliding on the Hampden turf, with some meaty slide tackles going in.
Shota Arveladze tried his luck with a fierce shot from 20 yards but Andersson was right behind it.
1-0: Hibs' Gary Caldwell slots home the first kick
1-0: Shota Arveladze blazes wildly over for Rangers
1-0: Stephen Dobbie hits the ball straight at Stefan Klos
1-0: Daniel Andersson saves from Michael Ball
1-0: Garry O'Connor's effort is blocked by Klos
1-1: Craig Moore nets a powerful strike
2-1: Scott Brown tucks the ball into the corner of the net
2-2: Christian Nerlinger calmly scores for Rangers
3-2: Tom McManus slots the ball home
3-3: Paolo Vanoli levels the scores after five kicks each
3-3: Matt Doumbe hits the bar with Hibs' first sudden-death kick
3-3: Andersson tips Zura Khizanishvili's effort on to the bar
4-3: Colin Murdock sweeps the ball to the left of Klos
4-3: Frank de Boer hits the base of the post
With 27 minutes gone Rangers sliced open the Hibs defence with a neat passing move that ended with Ronald de Boer being upended by Andersson.
Arteta took the penalty kick but the Hibs keeper made amends with a fine one handed save.
However, Rangers were ahead five minutes before half time when a simple pass through the middle had Hibs in trouble.
Mols ran on to Ross' delivery and swept the ball into the net from 15 yards.
Hibs' new signing Gary Caldwell found the side-netting with an ambitious free kick early in the second half and Garry O'Connor hit a tame shot at Klos from a tight angle.
At the other end, Andersson had to field a Christian Nerlinger long-range effort as both teams struggled to create clear-cut chances.
Hibs threw on Dobbie with 13 minutes left, and the substitute had scored within a minute when he thrashed home a pass from Riordan from 12 yards.
The Edinburgh side were galvanized by the goal and Rangers were pinned back - desperately defending for a frantic five minute spell.
Hibs players go wild after the penalty shoot-out
Ricksen was lucky to escape punishment when he elbowed Riordan off the ball, and Hibs had a strong penalty claim when Ross barged into O'Connor.
Hibs maintained their attacking momentum in the first period of extra time but, despite their endeavour, could not prise open the Rangers defence.
Hibs survived two penalty box scrambles early in the second half of extra time and Matthias Doumbe made a vital block to deny Mols a second goal.
Moore looked to have won the game in the 110th minute when he powered in a low drive but Dobbie popped up on his own goal-line to clear.
Both sides were exhausted in the final stages but play raged from end to end.
Both goalkeepers made two fine saves apiece in the penalty shoot-out, while Arveladze blazed the first kick over the bar and Doumbe hit the woodwork.
With the scores at 3-3, Colin Murdock tucked away his kick and Frank de Boer followed with a low strike that hit the post.
Hibernian: Andersson, Caldwell, Doumbe, Murdock, Edge, Scott Brown, Wiss, Reid, Thomson, O'Connor, Riordan. Subs: McManus, Nicol, Whittaker, Dobbie, Alistair Brown.
Rangers: Klos, Ross, Frank de Boer, Moore, Ball, Arteta, Ricksen, Nerlinger, Mols, Ronald de Boer, Arveladze. Subs: Ostenstad, Khizanishvili, Vanoli, Capucho, McGregor.
Referee: K Clark