Celtic responded by playing their visitors off it. It could hardly have gone better for Ronnie Deila as he took charge of his team at Celtic Park for the first time. For weeks the Norwegian had urged his players to play at a higher tempo, to be more assertive and to take their chances.
They belatedly did so and in spades, scoring six times and threatening to add several more. Towards the end of the first half especially, the pace and slickness of Celtic's passing moves would have had Deila purring. It was quite the show to put on for the watching Fergus McCann, who surely would have approved.
This was the perfect warm-up for Celtic's Champions League play-off match against Maribor on Wednesday, assuming there is no curve-ball tomorrow from the Court of Arbitration for Sport after Legia Warsaw's appeal.
There were strong performances all over the pitch for Celtic. Jason Denayer embroidered an accomplished debut with a goal after four minutes, Jo Inge Berget scored twice, Callum McGregor was lively, and Emilio Izaguirre was a permanent menace on the left wing. The stand-out performer, however, was Anthony Stokes, who can consider himself unlucky not to have scored.
But boy, did he try, the striker lashing in shots from various distances and angles that were either off-target or repelled by Radoslaw Cierzniak in the United goal. When Stokes thought he had finally scored from a free- kick early in the second half, he looked up to see Charlie Mulgrew darting off in celebration, having claimed the faintest of touches.
Poor Stokes wore the expression of a small boy whose puppy had just run away from home.
The only cloud on an otherwise sunny day for Celtic came in the last minute when substitute James Forrest pulled up with what looked like a hamstring injury. He and Adam Matthews, removed from the starting line-up close to kick-off, will likely miss the midweek trip to Slovenia.
That aside, this was quite the extravaganza from Celtic. The injured Scott Brown brought out the Premiership trophy before kick-off and then McCann, the man credited with saving the club from financial ruin, appeared to unfurl the league flag.
He greeted the rapturous reception by almost sheepishly offering a thumbs-up gesture to the fans, then ambled across the pitch to take a seat among them in the North Stand.
It wasn't such a great day for another returning Celtic hero. Jackie McNamara took his team to Glasgow harbouring aspirations of becoming the first Dundee United manager to win at Celtic Park since 1992, but his team never really gave themselves a chance with an abject defensive display.
Of the six goals conceded, three came from corners and another from a free-kick. Celtic were good value for their victory but they never really had to work for it as United stumbled from one blunder to the next. It was the least convincing performance at Celtic Park since the dancing Teacakes that pranced around at the opening ceremony of the Commonwealth Games.
Before McCann had taken his seat, Celtic were in front. United's game-plan was to try to get Gary Mackay-Steven in behind the Celtic defence and it worked once or twice, most notably in the second minute when the winger drilled in a low shot that whizzed past Craig Gordon's post. He probably should have scored and United never recovered.
Celtic went in front two minutes later. Kris Commons' corner wasn't adequately cleared, and Denayer showed composure to zip a shot into the top corner.
The second goal arrived after 28 minutes and effectively ended any prospect of a United shock. Commons was allowed to glide unfettered to the near post to glance in Stokes' corner. Celtic were now enjoying themselves and scored a third shortly after.
Paul Paton was dispossessed by Stefan Johansen and the Norwegian worked his way to a shooting position before rifling a low shot past Cierzniak.
There was no let-up in the second half. Mulgrew claimed the fourth, before Berget got his first goal, a close-range header from another Stokes corner after Efe Ambrose teed him up. A deflected John Rankin shot was the sole positive note for United on an otherwise dispiriting day but it was not the last word.
That went to Berget who converted from close range in the final minute, a sign that Celtic were not of a mind to let up.