In their last outing before next Sunday's showdown with Rangers at Ibrox, Celtic's winning performance was so impressive that it was hard to believe they had won only one of their previous nine away matches this season.
Celtic's sharpness and strength, driven by the will of champions in fear of losing their title, ensured Dundee's midfield and defence rarely enjoyed a moment's peace.
Even so, establishing a two-goal lead with the game only 12 minutes old and contriving other near things during a dazzling opening quarter was a thrilling surprise for those Celtic supporters at Dens Park yesterday.
The inspiration during this ascendancy came from Paul Lambert and Lubomir Moravcik, taking such control of the midfield that their partners in that area, Phil O'Donnell and Vidar Riseth, could turn their attention to forward tasks. It was no accident the latter pair should score the first two goals.
Moravcik began the damage after three minutes with a perfect chip from the right which just cleared Brian Irvine's head and allowed O'Donnell to steal in, take one touch with his right foot, then flick the ball past the advancing Robert Douglas with his left.
Lambert supplied Riseth for the second, holding the ball out on the left until he had the space to deliver a right-footed cross. The tall Norwegian arrived between Irvine and Steven Tweed, took off and bulleted his sixyard header high to the right of Douglas.
Celtic, especially in the first half, had such control that every time the home side cleared their lines, the ball came straight back.
The champions managed only one goal in the first 12 minutes of the second half, but that was mainly because of Douglas's good save from Mark Burchill when the striker had been released by Riseth's precise through pass.
Then Douglas scored, inadvertently, for Celtic. O'Donnell crossed perfectly from the left and Henrik Larsson headed down past Douglas. The stretching Irvine pushed the ball against his goalkeeper and it bounced back over the line.
Dundee had enjoyed their best spell just before that third goal. It was, however, more by physical endeavour than inventiveness, and they did not seriously bother the Celtic goalkeeper Jonathan Gould.
Phil O'Donnell hailed Celtic's win as the perfect warmup for next Sunday's Old Firm clash at Ibrox. "We won 3-0, and it could have been more, but the way we've played has been a big bonus for us," said O'Donnell.
"We've got a big game on Sunday now and we're looking forward to it. We'll go into it full of confidence."
Celtic beat Rangers 5-1 at Parkhead in the last clash of the Glasgow clubs and O'Donnell added: "We hope we can win this one too."
Skipper Tom Boyd said: "In our position we have to keep winning games and we played well tonight, showing our intentions right from the start. We had the chances to score a few more but we've come here and won 3-0 and I think we have to be very happy with that."
Celtic coach Jozef Venglos said he was thoroughly satisfied with his team's display. "We played very well, there was a lot of good passing and good co-operation among the players. I was pleased with the freedom of expression there was in the team today and I am sure people could see that on TV.
"The boys showed their quality and I believe in their quality. Hopefully we can show these qualities again next Sunday. It should be a good and exciting game and I believe in my players because they are all top quality."
Venglos explained that Simon Donnelly had been omitted from the squad as he was suffering from a muscle strain.
Dundee have suffered three defeats on the trot and manager Jocky Scott claimed his team went down because there was a lack of belief.
"Maybe our confidence has taken a knock but we will work hard and try and rectify it," he said. "I am obviously disappointed with today's performance, more so in the way we lost the goals. You cannot give Celtic that much room. Their movement was good and their passing and pace was excellent. In this mood they are very difficult to play against."
DUNDEE: Douglas; Smith, Irvine, Tweed, Rogers (Sharp, 63min); Adamczuk, McInally (Rae, 75), McSkimming; Anderson (Annand, 63), Grady, Falconer.
CELTIC: Gould; Boyd, Stubbs, Mjallby, Mahe; Riseth (McNamara 78), Moravcik, Lambert, O'Donnell; Larsson, Burchill (Brattbakk, 80).
Referee: J McCluskey (Stewarton).