Paul Burns was the hat-trick hero as Queens comfortably booked a place in the ALBA Cup semi-finals.
The midfielder struck from eight yards on 32 minutes after David Holmes had knocked on a David Weatherston cross.
Shortly after the interval, Burns cracked in a shot from a Ryan Conroy delivery and John Ovenstone added an unfortunate own goal.
Burns poached his third on the goal-line and Bob Harris rifled in an injury-time free kick for Queens.
The first half hour of the contest had been even, with the Second Division visitors going close through Kurtis Byrne and Conroy being denied by a good save from Michael Brown.
However, once Burns broke the deadlock the home side began to grow in confidence.
At 2-0 the men from Methil were still in the contest and Lee Robinson made important saves to keep out efforts from Byrne and Robert Lynn.
The contest was over when Ovenstone headed a Conroy cross into his own net, having been introduced as a substitute six minutes earlier.
The hat-trick moment for Burns came with 12 minutes remaining when applied the finishing touch from close in after Holmes had lifted another Conroy pass over the advancing Brown.
Burns got to keep the match ball for the first time in his career but Harris had the last say with an excellent free kick in the closing stages.
A clinical display from Queens over an enterprising Methil side who had plenty of the ball but sadly lacked punch.
Queens Mad man of the Match - It has to be Paul Burns with his magnificent hatrick.
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