Dundee United’s dreadful defending and Celtic’s excellent finishing combined to pile on the misery for the Tangerines at Tannadice.
Leigh Griffiths gave the Hoops the lead on 21 minutes after United centre-back Gavin Gunning fell on his backside instead of clearing the ball. There was a hint of offside about it but referee Bobby Madden let it go.
It was 2-0 six minutes later when the unmarked Jozo Simunovic got his head on the end of a Kris Commons freekick from the left, with home goalie Eiji Kawashima not covering himself in glory as he failed to cut out the cross.
The Tangerines hit back with a well-constructed goal on 31 minutes to give themselves hope.
A superb pass from John Souttar sent Simon Murray through on goal and the frontman picked his spot past Parkhead number one Craig Gordon.
However, the champions were 3-1 up just three minutes into the second half when Griffiths grabbed his second of the night. It was another bad one for United, with the marking leaving a lot to be desired as three opposition players – the ex-Dundee man, Commons and Armstrong – all stood free inside the area.
The best goal of the night was scored by Commons on 56 minutes, a volley that hammered home his side’s superiority. Once again, United were at fault as Scott Fraser got caught in possession just a short distance from his own box.
There had been a major selection blow for United in the hours before kick-off with the news that they would have to manage without striker Billy Mckay, who was given compassionate leave following a family bereavement.
They also had both Guy Demel and Mark Durnan serving suspensions.
All that added up to major changes, with manager Mixu Paatelainen making five in total from the team that kicked off against Airdrie in the Scottish Cup last Saturday.
Into the starting line-up came Ryan McGowan, Gunning, Souttar, Murray and Riku Riski, with Coll Donaldson and Chris Erskine dropping down to the bench.
Former United man Armstrong was in the Hoops’ midfield but Nadir Ciftci had to make do with a place on the bench, while Gary Mackay-Steven wasn’t even in the squad.
A tangerine smoke bomb was let off in the Eddie Thompson Stand by United fans as the teams came out.
There was a break upfield by the home team in the first minute but Fraser couldn’t get his foot around a Riski cutback.
Fraser then shot over from 25 yards and Armstrong fired wide for the visitors as the match opened up a bit.
Commons came even closer than those two when he let fly on nine minutes and Kawashima was happy to see the ball sneak by his far post.
Paul Dixon then hooked the ball clear after an Armstrong cross zipped in front of United’s goal a couple of minutes later.
It was all about Armstrong and he pounced on a breaking ball to race on and curled a shot just wide of the home goal.
On 21 minutes, the Hoops took the lead and the goal came gift-wrapped.
Gunning fell on his backside when he looked likely to clear and the loose ball was pounced on by Griffiths, who blasted the ball through Kawashima’s legs.
It was the former Dundee man’s 50th goal for Celtic in just 60 starts.
Just six minutes later, the champions were two ahead.
It was a simple goal from their viewpoint and another bad one for United, who failed miserably to defend a freekick from the left.
Commons took the setpiece and out came Kawashima, only to miss the ball completely. The unchallenged Simunovic – he was meant to be Gunning’s man – sent a bullet header into the back of the net.
To their credit, United kept the heads up and got one back on 31 minutes with a well-worked goal.
It was a cool finish from Murray, who nicked the ball past Gordon after being set up by a terrific pass from Souttar.
McGowan almost grabbed a leveller for United before the break but Gordon somehow managed to keep the ball out.
United were on the back-foot after the interval and Gunning was booked for pulling back Stefan Johansen with the home defence outnumbered.
Murray missed a decent chance for United at one end then up went Celtic to the other to restore their two-goal lead.
The home defence was all at sea once again, allowing Commons the luxury of missing the ball when unmarked only for Griffiths, also with no one on him, to fire into the United net.
Gunning then pulled a shot wide for the Tangerines but it was soon 4-1 as United were sliced open by a beautiful goal from Commons.
The ball was floated perfectly to him by Armstrong on 56 minutes and his finish was a piece of fine art a scissor-kick volley that gave Kawashima no chance.
Commons had the ball in the net on the hour but he was offside then United should have had a penalty on 66 minutes when sub James Forrest handled but Madden waved play on.
With four minutes left, Commons took a pass from Griffiths and rolled the ball inches beyond the far post.
United kept plugging away but it just wasn’t their night and they were put out of their misery by the final whistle.
Dundee United: Kawashima, Dillon, Dixon, Souttar (Paton 82), Rankin, McGowan, Murray (Erskine 73), Gunning, Spittal, Fraser, Riski (Dow 64). Subs not used: Zwick, Telfer, Spark, Donaldson.
Celtic: Gordon, Ambrose, Simunovic, Griffiths, Armstrong (Allan 69), Commons, Rogic (Forrest 60), Lustig, Johansen, McGregor, Tierney (Izaguirre 78). Subs not used: Bailly, Ciftci, Cole, O’Connell.
Referee: Bobby Madden.