Two goals from Gary Hooper helped Celtic to a convincing victory and undoubtedly stiffened manager Neil Lennon's resolve to get the best price possible for the striker if he is to leave Parkhead this month.
Before kick-off Lennon confirmed that his striker had turned down a new contract while also revealing that the club had rejected another offer from Norwich for the 24-year-old last week.
Hooper, who has 18 months left on his deal, showed why he is attracting increasing interest when he converted a Georgios Samaras pass in the 19th minute before midfielder Victor Wanyama headed in number two before the break.
Former Scunthorpe striker Hooper struck again 10 minutes from full-time to take his tally for the season to 22 before he set up substitute Scott Brown for the fourth as Dundee United, whose boss Peter Houston will leave at the end of the season, were left thankful that their defeat had not been even heavier.
Celtic who were first to benefit when Lassad Nouioui raced away on a counter-attack with the United rearguard chasing, and when he moved the ball wide to Samaras, his first-time pass to the unmarked Hooper saw him confidently beating United 'keeper Radoslaw Cierzniak.
The second came when Charlie Mulgrew's corner was cleared out to Mikael Lustig and when he swung a cross to the back post, the unmarked Wanyama powered a header back across goal and into the net.
Celtic started the second half with Lassad heading Joe Ledley's cross over from six yards and there was little to suggest United could stage a comeback. Celtic remained in control and dangerous on the break.
Ten minutes from time Celtic broke with pace again and skipper Samaras set up Hooper to score with a neat flick at the near post.
Dubliner Anthony Stokes replaced Lassad eight minutes from time to make his first appearance since August after recovering from an ankle injury, but it was Brown, on for Beram Kayal, who curled in goal number four after taking a Hooper pass, to leave the champions 12 points clear of Inverness at the top of the table.
However, the focus over the next few days at least, will remain on Hooper.