Chris Sutton helped himself to a double as Celtic rediscovered home comforts after their midweek disappointment in Milan.
The champions showed only a positive reaction to their Champions League defeat as they effectively wrapped up the three points before half-time.
Stilian Petrov was also on the scoresheet as Celtic killed the game and were content to stifle Dundee United after half-time.
In a whirlwind start, John Hartson had an early chance for the visitors from a Didier Agathe cross but could get no power in his header and Paul Jarvie gathered easily.
Barry Robson came within inches of the opener moments later when he curled a 20-yard free-kick past the defensive wall but the ball finished just outside the post.
United were by no means overawed and had a couple of strong penalty claims turned down by Hugh Dallas in the first half.
Joos Valgaeren's challenge on Stuart Duff looked a certain penalty but Mr Dallas decided otherwise, much to United's dismay.
But the home side found themselves two goals down before 17 minutes had elapsed.
United left Sutton unguarded at a Petrov corner and he scored with a simple six-yard header in the ninth minute.
Eight minutes later a clearance from David Marshall was helped on by Hartson and Petrov provided a crisp finish to make it 2-0.
Jim McIntyre almost pulled a goal back shortly afterwards but Valgaeren made a fine last-ditch block to keep Celtic's advantage.
It was end-to-end stuff and Juninho should have grabbed a third for Celtic in the 25th minute after Henri Camara rolled the ball into his path, but he dragged his shot wide when it looked easier to score.
Jarvie then made a fine save to prevent Hartson getting on the scoresheet after more good work from Camara.
Celtic had more of a cutting edge and looked capable of scoring every time they went forward, as Stanislav Varga shot narrowly over after a Petrov free-kick was blocked.
The champions moved further ahead with nine minutes of the first half left when Jarvie pulled down Camara in the penalty area and Dallas pointed to the spot.
Sutton made an expert job of the penalty, firing it low into the corner of the net.
United changed things at half-time with Derek McInnes replacing David McCracken and they showed immediate improvement.
But, if they looked more resilient, the home side struggled to get any sight of Marshall and Celtic were not unduly troubled.
The Bhoys seemed content to play out time as they shifted down the gears in the second half in the knowledge that the points were secure.
Dundee United had another penalty claim after 73 minutes when the ball appeared to strike the arm of Agathe but again referee Dallas was disinterested.
James Grady had a chance to pull one back at the death but mis-kicked and Marshall gathered comfortably.