For them, it was not just a return to form but a return of confidence, as O’Neill suggested to BBC Sport Scotland afterwards.
“It was delightful,” he said. “We played really well and won quite convincingly.
“The players have to do the playing and it’s been a strange old week. I’ve come back in again – perhaps to haunt them as much as anything else – but the players did brilliantly, absolutely brilliantly.
“The crowd were magnificent. Even moments when we were poor they kept with us. Today was great, there was a nice atmosphere. Now, being in a dogfight for the championship, we need the crowd behind us.
“It was all about winning but the performance was terrific – I don’t think I should overlook that. We played really well, got confidence back and it was lovely to win.”
In the ‘dogfight’ for the title the manager identifies, Celtic have their own veteran of such combats back in O’Neill.
With Liam Scales restored to the centre of defence, they looked organised and compact at the back, where previously they were porous in the extreme.
O’Neill placed round pegs in round holes against United, and the result?
Four different goal scorers, wingers in Yang Hyun-jun and Sebastian Tounekti who didn’t have to worry about being the last line of defence, and a midfield which provided control and the decisive second goal through Arne Engels.
No wonder those observing were full of compliments.
“They dominated totally from start to finish,” former Celtic goalkeeper Pat Bonner said on Sportsound.
“It was a lot more controlled in possession, very different to under Wilfried Nancy where it was very energetic, big intensity, creating chances and not taking them.
“It looked to me they were much happier in the formation and the positions they were playing. They controlled the game, they knew what they were doing and there was no confusion.
“The crowd were very appreciative of Martin being back. It sets them up for a run of four away games and it couldn’t be better.”