Goals from Rooney, McLean and a GMS brace booked the Dons a place in the quarter finals.
Following the result the quarter final draw took place at Pittodrie. The Dons were drawn a home tie against Kilmarnock which will be played on the weekend of 3rd/4th March.
Derek McInnes named an unchanged side from the team that beat Hamilton 3-0 last Saturday in the Ladbrokes Premier League.
Having beaten St Mirren in the fourth round of the Scottish Cup previously, The Dons welcomed second placed Championship side Dundee United to Pittodrie, the first time in seven years that Pittodrie has hosted two Scottish Cup home games consecutively.
Dundee United got things underway at a very cold Pittodrie and there was also a stiff breeze that would make things difficult for both teams.
Aberdeen started brightly winning a corner in the first minute which came to nothing. On five minutes the Dons had their first half chance, Scott McKenna headed McGinn?s corner just wide.
Moments later Mark Durnan received the first booking of the afternoon, bringing down Shinnie as the home side looked to counter.
On eight minutes Adam Rooney had a golden chance to open the scoring. GMS intercepted a loose ball just outside the Dundee United penalty and fired a shot on goal. Lewis could only parry the ball out to Rooney who looked set to score but his shot was blocked and ricocheted out for a corner. From the resulting set piece Ryan Christie had a shot from long range that just curled wide at the near post.
The Dons continued to dominate and eventually took the lead in the 19th minute. Running down the right Kenny McLean hung up a cross to the back post. GMS met it and volley into the ground, his shot looked goal bound but needed the helping head of Adam Rooney who nodded home from a yard out.
Stanton was booked for a nasty foul on McGinn straight after the restart as the Dons continued to dominate the opening quarter of the cup tie.
Gary Mackay Stevens made it 2-0 to The Dons on 26 minutes. High pressing from the Aberdeen midfield forced the visitors into a mistake at the back, allowing McGinn to pinch the ball off Slater.
McGinn had the awareness to slip in GMS who showed great composure to slot past Harry Lewis and double Aberdeen?s lead.
But then similar to the St Mirren game, out of nowhere the visitors pulled one back through Sam Stanton just after the half our mark. After O?Connor failed to get enough distance on his clearance.
The United midfielder found himself running through on goal following the poor clearance and some quick first time passing. He calmly slotted home past Woodman to reduce the deficit.
Their lead didn?t last long.
From a United throw in, Christie intercepted and found a yard of space after a beautiful piece of skill. His cross was expertly met by Kenny McLean, who glanced his header into the far corner and restoring the two goal cushion. A really fine goal.
Both Shinnie and Andrew Considine went into the referee?s book for late challenges. Considine?s foul means he will miss the quarter final tie against Kilmarnock due to an accumulation of bookings.
After winning the goal of the round award for his strike against St Mirren, GMS nearly had another strong candidate on 38 minutes. Twisting and turning down the left he fired a vicious strike towards the top corner but Harry Lewis pulled off a fine save at the near post to deny the winger and keep the score at 3-1 going into half time.
Half Time: Aberdeen 3-1 Dundee United
The Dons got the second half underway and looked in the mood to give the 11,611 more goals to cheer.
Five minutes into the second half Rooney had a chance to add a fourth. Clever work from Christie and Shinnie down the left allowed Rooney a shooting chance on the edge of the area but he blazed his shot over the bar.
O?Connor and Woodman almost had a problem when miscommunication saw Woodman rush off his line whilst the Dons central defender still attempted a pass back. The keeper in the end did very well to divert the ball to safety with his foot.
On 55 minutes Gary Mackay Steven added his second and Aberdeen?s fourth of the afternoon. Great play from Ryan Christie, letting the ball run across his body, allowed him to run at the United back four. GMS made a supporting run alongside Christie who unselfishly slipped him in. The Dons wingers right footed shot had too much power for Harry Lewis and the ball flew into the roof of the net at the near post.
The game should have been finished then but Aberdeen took their foot off the gas and United pulled another one back with twenty minutes to play. A good run from Billy King had the Dons defence back peddling. King found Paul McMullan who curled his shot past Woodman into the far corner.
Following their goal, the visitors grew in confidence enjoying more possession and territory inside the Aberdeen half.
With 15 minutes left GMS nicked the ball off Robson and looked to counter, but the winger was brought down and Robson went into the book for his troubles.
McInnes made his first change of the day on 81 minutes. Gary Mackay Steven received a standing ovation as he was replaced by Dominic Ball.
Ball made an positive impact, after overlapping Adam Rooney he played a great ball across the penalty area to Christie who blazed his shot over the bar from 12 yards out ? a real let off for the visitors.
United threw everything at The Dons in final few minutes and they nearly pulled another one back. Woodman pulled off a great finger tip reaction save after the ball deflected off O?Connor inside the six yard box.
Adam Rooney was replaced by Nicky Maynard in the final few minutes of the game as the Dons saw out the remainder of injury time without any scares.
Aberdeen travel to Edinburgh next weekend to face Hibernian in the league before the visit of Celtic to Pittodrie on Sunday 25th of February.
Full Time: Aberdeen 4-2 Dundee United