Celtic kept up their revived pursuit of Rangers when Gary Hooper scored his 13th goal of the season at Tannadice to maintain his team's run of domestic form, which now extends to five league victories on the bounce.
If Neil Lennon's players went off the boil somewhat after the break, they still had enough in the tank to see off a young United side.
Celtic had never failed to score in a league match at Tannadice since the SPL began in 1998 and it took them only 12 minutes to extend the tradition.
United were deployed in a 4-5-1 formation intended to give them an advantage in midfield, but Celtic's fluency was not hindered for long as Georgios Samaras demonstrated with a break from the left that bore him into the box to hit a rasping angled drive which skimmed just beyond the far post.
The movement of Hooper and his rival for the status of top scorer, Anthony Stokes, was a perpetual difficulty for the United central defence, especially when James Forrest supplemented the Celtic forwards with his guile and direct running from midfield.
It was just such a circumstance put Celtic in front with a high-tempo move that saw Forrest prompt Hooper, whose response was to slip away from Gavin Gunning and finish with a trim low drive across Dudan Pernis and into the far corner of the net.
Forrest should probably have doubled Celtic's advantage when Stokes put him in for a full-blooded drive that was, however, aimed directly at Pernis, who clutched gratefully. United's response was to switch to 4-4-2, with Johnny Russell pushed up alongside Jon Daly.
It made no difference to United's outstanding weakness -- that their frequently inventive build-up was not transformed into menace where it mattered -- and the uncomfortable statistic is that Fraser Forster did not have to make a single save, unlike Pernis, who had to keep his wits about him as Celtic renewed their pressure in the closing minutes of what had otherwise been a dull second half.
By that time Scott Brown had made his second substitute appearance in four days, having come back from a long lay-off.
Between times the Celtic captain had at last concluded his negotiations over a renewal of contract and had committed himself to the club until the summer of 2015, an event greeted by the travelling support with a celebratory chorus on the midfielder's appearance. (© Daily Telegraph, London)