Championship trophies have never been handed out on the basis of artistic merit. Which in Scotland is probably just as well. A day after Rangers toiled in defeating Dunfermline at Ibrox, Celtic ground out a victory. To the visitors' credit here, there never seemed any genuine likelihood of Dundee United clawing their way back into the game. Still, the second half in particular was grim, with both sides lacking inspiration.

Neil Lennon, the Celtic manager, admitted his team became "sloppy in the final third". Unsurprisingly, it was two defensive players – Daniel Majstorovic and Victor Wanyama – whom Lennon heaped praise upon.

"Our back four and our midfield gave us a great platform today," Celtic's manager said. In the league, Celtic have now kept four clean sheets in their last six matches, with the improved form of Majstorovic – once ridiculed even by his own club's supporters – a key factor.

The last time Gary Hooper scored a Celtic winner at Tannadice, in October last year, the controversial fall-out from the reversal of a penalty award dominated Scottish football's news agenda for months.

There will be no such discussion about this match, although there was a small element of officialdom intrigue and Hooper was again a key figure. Calum Murray was supposed to be the referee but traffic problems – an accident involving a car and a horse box – delayed his journey to Dundee sufficiently that he had to be replaced by Craig Thomson.

Celtic's start was brisk. Hooper collected a James Forrest pass before sending a fierce, low shot into the United net. It was an excellent goal – and one which wasn't in keeping with so much that followed.

Within 30 seconds of the kick-off, Anthony Stokes had only narrowly failed to send Celtic in front, and Forrest passed up another opportunity after Hooper's goal.

Yet by half-time Celtic's tempo had noticeably dropped. United, for all that they had spells of possession, did not have the guile to do anything about that; the hosts failed to create a single clear-cut chance throughout the 90 minutes.

Celtic fared only marginally better. Forrest came the closest to doubling their lead, three minutes from time, but blasted wide of the United goal.

Lennon introduced Scott Brown, his captain, with 23 minutes to play. The midfielder had ended a protracted contract saga by signing a new deal to remain at Parkhead on Saturday. "It is a tremendous boost," said Lennon of the Brown scenario being resolved. "He has always been committed to the club and I was always confident we could get him signed up."

Lennon said his removal of Glenn Loovens was because of a calf injury, despite the Dutchman not looking altogether happy about being substituted.

"I don't think we played anywhere near our capabilities," said Peter Houston, the United manager. "The first 20 minutes were good but we lost a poor, poor goal.Technically we were very poor today. Today the second touch seemed to be a tackle.

"It is unlike our players to be kicking the ball out of the park with nobody near them. We didn't create anywhere near as many chances as we wanted to. After the goal it was a poor match."

Man of the match Victor Wanyama (Celtic)