The win for the home side was helped immeasurably with an unfortunate early red card for visiting keeper William McCulloch.
This was the first time that Aberdeen had scored five goals in over three seasons, the last coming when they defeated lower league Brechin City in a CIS Cup tie and Dons boss Jimmy Calderwood will now face former club Dunfermline in the quarter-finals.
Aberdeen were first to show in four minutes when Sone Aluko glided past Paul Nugent before lofting the ball to the far post. Tommy Wright out-jumped his marker but his downward header was parried onto the post by keeper McCulloch who held the ball at the second attempt.
Disaster struck for the visitors in the next minute. Neat footwork by Javan Vidal saw him skip past Shaun Fagan before playing in a superb throughball to Aluko.
The diminutive wide-man was on to the ball in a flash, as he lifted it over the advancing McCulloch who instinctively handled the ball. However, as he was a long way outside his area he left referee Steve Conroy no option but to brandish a red card.
Aberdeen finally broke the deadlock on 11 minutes. Aluko picked up a loose ball out wide on the left and quickly fired a cross into the area.
Visiting centre-half Greig McDonald made a hash of his clearance, only succeeding in playing the ball on to Wright who swivelled and clipped his effort into the roof of the net from 11 yards for his first goal in Aberdeen colours.
Aberdeen extended their league five minutes later. Strikers Lee Miller and Wright combined to pick out Chris Maguire. The youngster held the ball up long enough to pick out Vidal who simply passed the ball into the corner of the net from 16 yards.
The visitors were in disarray again when Aberdeen grabbed a third goal on 29 minutes. Aluko pounced on a loose ball after hesitancy by Nugent. From an acute angle his cross-cum-shot took a slight deflection off McDonald and ended up beating Michael Brown at his near post.
On 43 minutes Maguire and Richard Foster combined well on the right, before the latter's ball into the box found Wright whose squirmed effort fell wide of the post.
Aberdeen striker Maguire finally got his name on the score-sheet on 82 minutes. He was on hand to nod home a Charlie Mulgrew corner which sub keeper Brown got a hand to but couldn't keep out.
Aberdeen went nap in the 84th minute. Tenacious play by Maguire on the halfway line saw him dispossess Jonathan Smart before carrying the ball 30 yards, gleefully slipping the ball past Brown and into the unguarded net.