Tommy Johnson's early goal saw Celtic lose no time in taking control of the clash with Dundee.
Dundee were second best for most of the half, although Claudio Caniggia still caught the eye.
It took Celtic just six minutes to take the lead in a match which could take them to the brink of the title.
Johnson was the man who scored, poking it past goalkeeper James Langfield, who was a late replacement after first choice Marco Roccati injured himself in the warm-up.
Alan Thompson started the move down the left side of midfield with a long ball that found Henrik Larsson in a surprising amount of space and it was the Swede's cross that set up Johnson.
Langfield had already been required to make a first-minute save from Larsson after Lubo Moravcik, the only change from the side that started at Aberdeen on Sunday, put him behind the Dundee defence.
Then he was needed to get in the way of Johan Mjallby's volley after the ball had rebounded off Barry Smith.
Larsson was soon hunting his 48th goal of the season but saw a shot hit a defender and Johnson's feet were in a tangle when the rebound fell his way.
Dundee were already under the cosh in a game they had to win to make sure of a place in the top six.
Mjallby and Juan Sara clashed heads as both challenged for a high ball in the Celtic box.
Larsson fired a free-kick well over before needing treatment following a clash with Chris Coyne.
He recovered to cut in and fire a shot wide as Celtic continued to dominate.
Caniggia, the man Martin O'Neill admires but says he had not tried to buy, was at the centre of most of Dundee's counter-attacks.
Giorgi Nemsadze's ball through the middle found him in the box but the ball bounced away from him.
Larsson won a 50-50 challenge in the box and the ball fell perfectly for Johnson in front of goal but the striker miskicked completely and the chance was gone.
A Dundee corner saw Caniggia rise to flick a header across goal and wide.
Didier Agathe beat Marcello Marrocco and Beto Garrido down the right and his cross found Moravcik on the edge of the area but, with all the goal to aim at, he blazed over.
At the other end, Sara's overhead shot was deflected away for a corner.