Celtic ended a momentous week in which they won the right to face Barcelona once more in the Champions' League, with two new signings and three points from a late goal in Dundee.
After Israel international midfielder Nir Biton moved to Parkhead from FC Ashdod on Friday, Finland international striker Teemu Pukki, 23, was signed for £3m from Schalke 04 yesterday.
Neither played in this scrappy game at Tannadice, which looked to be drifting towards a draw when Anthony Stokes was brought down by United defenders Stuart Armstrong and Keith Watson on the edge of the box with just three minutes left of normal time.
Stokes, who had set up James Forrest for the Champions' League clincher in the 3-0 win against Shakhter Karagandy at Parkhead on Wednesday night, picked himself up and curled the free-kick over the wall, past Radoslaw Cierzniak and in off the post.
Celtic's manager Neil Lennon and Dundee United's boss Jackie McNamara both accused opposition players of "reckless" tackling.
The Celtic defender Mikael Lustig was carried off on a stretcher early in the second half after appearing to fall awkwardly following a hefty challenge by defender Gunning.
Lennon said: "I thought the challenge on Mikael was reckless to say the least. There is no fracture thankfully, it might be ligament damage. It is a relief because he is a top player."
But McNamara countered: "I think he went for the ball and they came together. I think a reckless challenge would be Scott Brown on Stuart Armstrong, I would say that was reckless."
Lennon also warned that English goalkeeper Fraser Forster, named this week in Roy Hodgson's England squad for the World Cup qualifiers, is not for sale.
"Fraser's not for sale. We had no confirmed bids for him," Lennon was reported as saying. "We have actually written a letter to one club, just warning them off basically."
Dundee United (4-4-2): Cierzniak; Watson, Gunning, Dillon, Robertson; Mackay-Steven, Paton, Rankin, Armstrong; Goodwillie (Gauld, 71), Ciftci. Substitutes not used McCallum, Butcher, Wilson, Souttar, Erskene, Graham.
Celtic (4-4-2): Forster; Matthews, Ambrose, van Dijk, Izaguirre; Boerrigter (Rogic, 83), Brown, Ledley, Lustig (Balde, 58); Stokes, Commons. Substitutes not used Zaluska, Mouyokolo, Herron, Atajic, McGeouch.
Referee Crawford Allan.