The Dons, who have been dumped out of the Scottish Cup by lower league sides in the last three seasons, eased into the fifth round with a comfortable win over the Second Division outfit.
Maguire struck three times and Scott Vernon grabbed another in a ruthless first half performance from the Dons that earned them an unassailable 4-0 lead. Vernon added a fifth after the break and substitute Josh Magennis netted a late sixth as the Pittodrie side, already with a League Cup semi-final to look forward to, booked their place in the next round.
Craig Brown made one enforced change for the match with Derek Young stepping in to replace Yoann Folly who suffered a season-ending injury in the 1-1 draw against Dundee United last week.
Former Don Stevie Crawford led the line for the part-timers, who had not played since a 6-0 thrashing of Stenhousemuir on December 11 last year.
Midfielder Robert Sloan, who was part of the Raith Rovers side that knocked Aberdeen out of the Scottish Cup last season, was also handed a place in the starting XI by boss John Robertson.
The Dons got off to the perfect start after 13 minutes when David McNamee was allowed too much time to pick out a cross for Maguire who guided the ball on the volley expertly into the corner of the net.
The Fifers had to make an early change after 16 minutes when Scott Durie came on for the injured Steven Campbell.
The Methil outfit almost restored parity when, firstly, David Muir's angled header from a Sloan corner went inches wide before Jamie Langfield made a brave safe to prevent Dylan McGowan bundling the ball over the line.
The Dons doubled their lead after 24 minutes when Vernon latched onto McGowan's woefully short pass back and, although his shot was kept out by East Fife stopper Michael Brown, Maguire was on hand to gleefully slam the rebound high into the roof of the net.
And within half an hour it was three for the Dons when Ryan Jack breezed down the wing before drilling a low cross to the near post for Vernon to prod home.
Maguire completed his hat-trick just before the break when he raced onto a Sone Aluko pass, cut inside to leave substitute Durie trailing and maintained his composure to roll the ball under the helpless Brown.
The second half started in a similar fashion with the Dons pushing forward at every opportunity and Aluko was inches away from adding a fifth when he failed to connect with Jack's enticing delivery.
Sloan stung the palms of Langfield with a powerful long range effort and Bobby Linn curled a fine effort just wide of the post as East Fife enjoyed more possession in the second period.
But with less than 10 minutes remaining the part-timers conceded again when substitute Magennis laid the ball into Vernon's path who made no mistake from 10 yards out.
And Magennis completed the scoring in injury time when he beat the East Fife offside trap to round Brown and tap the ball into the empty net.