The part-timers were reduced to 10 men within four minutes when Willie McCulloch was sent off for handling outside his box.
Tommy Wright and Javan Vidal grabbed their first goals for the Dons with clinical finishes before the hard-working Sone Aluko grabbed a third after 29 minutes.
East Fife defended resolutely in the second half but a Chris Maguire double added to their misery late on.
Lee Mair and Wright replaced injured duo Zander Diamond and Darren Mackie for Aberdeen, while Maguire and Aluko also returned with Derek Young and Stuart Duff dropping to the bench.
The Fifers, who had not played since they lost 3-0 to Peterhead on January 31, made three changes with Goran Stanic, Jonathon Smart and Chris Templeman preferred to David Muir, Paul Stewart and Paul McManus.
The Second Division outfit had a disastrous start to the game when they were reduced to 10 men with less than four minutes on the clock.
McCulloch raced out of his box to close down the onrushing Aluko but when the East Fife goalkeeper handled the Aberdeen midfielder's shot, referee Steve Conroy had no option but to produce a red card.
The unfortunate Stanic was sacrificed to bring on substitute goalkeeper Michael Brown but the East Fife deputy was helpless to prevent the Dons taking the lead after 11 minutes.
Aluko, who gave Paul Nugent a torrid time, crossed for Wright whose first-time effort found the top corner of the net for his first goal for the Dons.
Vidal then grabbed his first strike for Aberdeen five minutes later. Maguire and Aluko linked up brilliantly before releasing the young Englishman who slotted the ball past Brown.
Aluko added a third for the home side when he pounced on Nugent's hesitancy before racing in on goal and his shot deflected off Greig McDonald past Brown at his near post after 29 minutes.
East Fife's Shaun Fagan was very lucky to avoid joining McCulloch for an early bath after appearing to throw a punch at Aluko but the offence went unpunished.
Wright could have netted his second just before half-time when Richard Foster found him with an intelligent pass but the Englishman's effort went just wide.
Aberdeen continued where they left off after the break with Mark Kerr racing on to a centre from Maguire but the former Dundee United midfielder's touch deserted him at the vital moment.
East Fife made their first change after 54 minutes with David Muir replacing Nugent.
The substitute had a great chance to pull one back for the Fifers when he raced onto a Templeman pass but blasted his shot into the side-netting.
A great save by Brown prevented Lee Miller increasing Aberdeen's advantage with a header from another deadly delivery from Charlie Mulgrew.
Templeman had a driven shot from distance comfortably saved by Jamie Langfield before promising Aberdeen prospect Peter Pawlett replaced Vidal after 65 minutes.
With the game comfortably secured Aberdeen then introduced Michael Paton for Miller after 72 minutes.
Maguire spurned a great opportunity after 75 minutes when he darted onto a Langfield clearance but blasted well over the bar with only the keeper to beat.
The impressive Aluko was replaced by Derek Young four minutes later with East Fife withdrawing Fagan for Paul Stewart soon after.
The home side eventually got their fourth with less than 10 minutes to go when Maguire headed home a Mulgrew corner.
The young striker got his second after 84 minutes when he won the ball on the halfway line before racing through with the ball and slotting the ball coolly past Brown to seal the victory for the Dons.