John Robertson's Fifers won 4-3 in a shootout at Pittodrie after an action-packed match had finished 3-3 after extra time.
The Dons, who have made a habit of exiting cup competitions to lower league sides in recent seasons, ran out 6-0 winners when the sides met in the Scottish Cup in January but this proved to be a much closer affair.
An upset looked on the cards when the part-timers, currently bottom of the Second Division, broke the deadlock when Ryan Wallace smashed the ball home after 31 minutes.
Rory McArdle headed home an equaliser five minutes before half-time and Darren Mackie gave the Dons the lead two minutes after the break.
Two goals in as many minutes from Matthew Park and Robert Sloan gave the Fifers the initiative, but Fallon forced the game into extra time when he netted from the spot after Mohamed Chalali had been brought down by Steven Hislop.
When extra time finished goalless, it was the Fifers who kept their nerve in the penalty shoot-out, with Chris Clark missing the decisive spot-kick for the Dons.
Aberdeen made seven changes to the side that drew 2-2 with Kilmarnock on Saturday, with only skipper Richard Foster, Kari Arnason, Ryan Jack and Andrew Considine retaining their starting berths.
East Fife also shuffled their pack with Stevie Campbell and Sloan stepping in for trialist Chris Innes, who was ineligible, and the absent Craig Johnstone.
The Dons went close to opening the scoring after 13 minutes when Arnason's glancing header from Foster's tantalising corner kick drifted just past the post.
East Fife survived the early onslaught and created a chance of their own when Wallace weaved past two Dons defenders before unleashing a powerful shot from 25 yards which flew over the crossbar.
John Robertson's side had a lucky escape after 27 minutes, when Vernon turned the ball home after Mark Ridgers spilled Jack's low drive but the goal was ruled out for offside.
But it was the Second Division side who took a shock lead after 31 minutes when Robert Ogleby crossed for Wallace, who rammed the ball high into the net.
However the Dons restored parity five minutes before the break when McArdle rose highest to nod home a Jack free-kick.
And the hosts could have taken the lead before the break when Vernon slid the ball across the face of goal for Magennis, who could only divert the ball onto the post.
The Dons gained the upper hand within two minutes of the restart when Ridgers was only able to push Vernon's shot into the path of Mackie, who steered the ball into the unguarded net.
But the Fifers were not to go down without a fight and they levelled the scores in spectacular style when Park's first-time effort from 25 yards sailed straight into the top corner after 54 minutes.
And they regained the lead two minutes later when Wallace played in Sloan, who slotted the ball past David Gonzalez.
But the Dons were handed a lifeline when Chalali was brought down in the box by Steven Hislop deep into injury time and Fallon stepped up to force the game into extra time.
Neither side could find a winner in extra time so it was left to penalty kicks to decide the outcome, with the Second Division side emerging victorious as Fallon, Magennis and Clark all failed to score for the Dons.