The Scottish champions stayed on top of the table by a point after a Henrik Larsson goal, an own goal from Scott Leitch and Valgaeren‘s effort.
Celtic even had the luxury of the Swede missing an early penalty while Dirk Lehmann gave the visitors a deserved consolation.
A relieved O’Neill said: ‘‘They did well the first half especially, although we didn’t convert an early penalty. They have three great chances in that half, but Robert Douglas made some good saves so I was obviously pleased to have won.
‘‘They had that five-minute spell which could have made it very awkward and maybe the midweek excursions did affect the players.
‘‘It was a big effort on Thursday evening and you never know how much it takes out of you until you get out there.
‘‘But the players wanted to play and I made four changes and I was delighted to have won the game.’’
Motherwell manager Terry Butcher last night put a comforting arm around Shaun Fagan and told the youngster he did not even get a hug when he was sent off against Celtic.
The 18-year-old, who was the match-winner for his side when they faced the Glasgow giants earlier in the season, was dismissed after picking up a second yellow card for punching the ball into the Celtic net with his side down 3-1 at Parkhead.
Former Rangers defender Butcher tried to cheer up the distraught’’ player up by telling him that Maradona famously got away with a similar goal against England. But he admitted his player was fortunate not to be given a straight red for kicking out at Joos Valgaeren earlier in the game.
Butcher, who was sent off against Celtic in his playing days with Rangers, revealed: ‘‘He is obviously very upset and distraught by it. But he was crazy in the first incident when he got booked on the far side and then he couldn’t quite get there with the head and his hand comes up.
‘‘The referee had no alternative but to send him off so I can have no complaints with John Rowbotham about that.”
That was the bottom club’s fourth sending-off in two games, after having David Partridge, Daniel Sengewald and Stephen Pearson dismissed at Hibernian last week.
But Butcher is confident his side can make up the five-point deficit at the bottom even though he joked that the Scottish FA’s head of discipline Drew Herbertson might have to pick his team for the midweek game against Hearts.
CELTIC: Douglas, Valgaeren, Balde, Crainey, Agathe (Sylla 75), Lambert, Thompson, Fernandez, Guppy (McNamara 75), Larsson (Maloney 75), Hartson.
MOTHERWELL: Dubourdeau, Corrigan, Kinniburgh, Dempsie (Quinn 67), Hammell, Ferguson (Khaled 65), Fagan, Leitch (McDonald 84), Adams, McFadden, Lehmann.
Referee: J Rowbotham (Scotland).