David James' Kerala side came into the second leg in Chennai as firm favourites following a 3-0 success in the home tie on Saturday, but Chennaiyin - who had topped the table at the end of the regular season - mounted a stirring fightback to force extra-time.
In a remarkable game that saw a missed penalty, a farcical own goal and three red cards, Kerala eventually prevailed 4-3 on aggregate courtesy of Stephen Pearson's strike three minutes before the end of the extra period.
The visiting Blasters - the lowest ranked side coming into the play-offs - were reduced to 10 men inside half an hour when James McAllister was sent off after picking up a second caution.
They fell behind three minutes before the interval when Mikael Silvestre stooped to head in Marco Materazzi's left-wing free-kick.
Five minutes into the second period, Sandesh Jhingan's foul on Jean-Eudes Maurice afforded Materazzi the chance to reduce the overall deficit to one from the penalty spot.
The World Cup winner sent his kick low into the bottom left-hand corner but, after being ordered to re-take it due to encroachment, he went the same way again and missed the target.
With time running out for the hosts, a mix-up between Jhingan and goalkeeper Sandip Nandy saw the defender chest a long ball into his own net and, in the final minute, Jeje Lalpekhlua converted Bernard Mendy's cross - with a suspicion of handball - to level the aggregate score at 3-3.
Materazzi picked up his second caution in quick succession in the first period of extra time to even up the numbers, before Pearson shrugged off two challenges and placed a low finish into the net to spark scenes of delirium among the Kerala players.
Chennaiyin's misery was complete a minute before the end when substitute Bojan Djordjic was sent off for dissent, capping a remarkable two hours of action.
There was much less incident in the second semi-final, which saw Goa and Kolkata play out a dour 0-0 draw in the second leg to complete 180 minutes of goalless action.
After extra time failed to produce a winner, the Indian Super League saw its first penalty shootout, which was won 4-2 by the visitors Kolkata.
Goa's Andre Santos blazed the first effort over the crossbar, before Haroon Fakhruddin struck the woodwork with the home side's third.
That allowed Kolkata captain Borja Fernandez to convert the winning kick and book a date with Kerala in Saturday's showpiece.
