Julian Joachim struck twice on his 32nd birthday after Simon Johnson had opened the scoring from the penalty spot.
But Leroy Lita twice levelled, before Hungarian defender Peter Mate marked his debut with a third equaliser by appearing to bundle home Glen Little's penalty with his hand.
David Stockdale saved Steven Hunt's penalty but was adjudged to have moved from his line, allowing Hunt to fire home the re-take and tee up a spot-kick win that was sealed by Andre Bikey.
After a dreary start in a half-empty Madejski Stadium, the game suddenly burst to life on 20 minutes.
David Rowson tried his luck from the edge of the area and, though his shot deflected wide off Hunt, Craig James' resulting corner saw Darlington captain Darren Holloway tugged back in the area by Brynjar Gunnarsson.
Johnson gratefully fired home from the penalty spot with his effort creeping under the body of keeper Graham Stack.
It took Reading 11 minutes to find an equaliser and, when it came, it was presented to them on a plate by Holloway.
The Darlington skipper headed a long ball back towards his own goal under pressure from Shane Long not realising that Stockdale was already well off his line.
The wayward header fell kindly to striker Lita – the only survivor from the Reading team which started at Sheffield United on Saturday – and the front man had the simple task of stroking into an empty net.
Reading's reprieve was short lived as Darlington reclaimed the lead within three minutes.
Former Aston Villa striker Joachim set off on a run down the right, leaving first Hunt and then Ulises De La Cruz in his wake before teeing up Johnson.
And, though the striker's shot was blocked by John Halls, the ball rebounded kindly for Joachim to fire home.
Instantly, Reading pegged back the League Two side once more.
John Oster played a neat pass through the middle of the defence allowing Lita to step forward and slide home his second.
Johnson should have put Darlington back in front midway through the second half but flicked a free header across the face of goal before Joachim struck again to give Darlington the lead for the third time in the game.
Rowson's corner was rolled into the path of Joachim who hit a superb side-foot finish into the top right-hand corner of the net.
That predictably heralded a cavalry charge from the home side as Reading poured forward in search of another equaliser.
Hunt's neat free-kick was superbly tipped on to a post by Stockdale, but when Darlington right-back David Duke was sent off for tripping substitute striker Kevin Doyle as he ran on to Hunt's through ball, the visitors faced an uphill task to hang on.
Hunt lifted the free-kick over the bar and Oster then saw a shot grabbed at the second attempt by Stockdale as the ball threatened to fly over his head.
And when the third equaliser came two minutes from time it was a controversial breakthrough as defender Mate appeared to use his hand to bundle in Little's corner at the far post.
The Royals created countless chances to complete the comeback in extra time but were continually denied by defiant Darlington defending.
Kalusivikako Ngoma was fortunate not to concede a penalty when he slid in to stop Long but ultimately it was from the spot that the game was decided.