The former Scunthorpe striker pounced in the 12th minute, taking a James Forrest pass inside the United box before drilling the ball low past Dusan Pernis.
Pernis then made a good save from Forrest to prevent the visitors adding to their lead in a first half which they dominated.
The second period was an anti-climax with neither goal really threatened, but it was a deserved win for the Hoops to keep the pressure on the champions with their fifth straight SPL win, which allows them to go into next week's game against Hearts with confidence.
Craig Thomson took over refereeing duties from Calum Murray, who reportedly got stuck in traffic and there were also changes in the Celtic side.
Midfielder Joe Ledley was ruled out with an ankle injury and was replaced by right-back Cha Du-ri while Hooper returned at the expense of midfielder Ki Sung-yueng, who started on the bench.
Skipper Scott Brown, who has signed an extended contract which keeps him at Celtic Park until 2015, also started as substitute.
United kept the same starting line-up which drew 0-0 with Motherwell last week with captain Jon Daly leading the line, and he looked an exposed figure for much of the first half as Celtic dominated.
Before a minute had elapsed, Georgios Samaras raced into the penalty area past United stopper Garry Kenneth and fired the ball across goal, with Anthony Stokes sliding in and only missing by inches.
The next chance came in the seventh minute when Forrest's cross from the right was headed over by Stokes, but the opener from Hooper was on its way.
In the 12th minute, as the Parkhead men pressed again, Forrest set up the former Scunthorpe player inside the United box and he rifled a low drive from 16 yards past Dusan Pernis and into the far corner of the net.
The only surprising thing was the visitors failed to add to their tally before the interval.
With Beram Kayal and Victor Wanyama dominating the midfield for Celtic, the flow of traffic continued towards the United goal and Pernis was called into action when Stokes played in Forrest and the keeper made a decent block from the Scotland winger's close-range drive.
Midway through the first-half United right-back Robbie Neilson got a header in from a John Rankin cross after Samaras had earlier conceded possession at the edge of his own box, but Celtic keeper Fraser Forster saved with ease.
Celtic again broke swiftly but, from 10 yards out, Stokes took a wild swipe at Forrest's cross and the ball flew high and wide.
In the 34th minute United midfielder Scott Robertson's attempted pass back from the halfway line was short allowing Stokes a chance to go through, but the Tannadice defence recovered and ultimately the danger was snuffed out.
The start of the second period did little to suggest United were going to come back into the game.
Celtic continued to dominate possession, playing at least one gear up from the Tannadice players although the slender advantage the Parkhead men held offered little room for error.
Just after the hour mark, Stuart Armstrong replaced Robertson and Lauri Dalla Valle came on for Gary Mackay-Steven as United boss Peter Houston tried another approach.
Brown then came on for Glenn Loovens in the 67th minute with Wanyama moving back from midfield to the centre of defence where he continued to excel.
United continued to rack up their unforced errors but Celtic could not capitalise and the game was in danger of drifting towards a tighter conclusion than the early stages had promised.
Stokes was replaced by Ki in the 77th minute as Lennon tinkered with his formation again.
Former Celtic player Willo Flood had an effort from the edge of the bar which flew harmlessly over, before Forrest missed the target from 16 yards at the other end.
Celtic's early dominance had disappeared but United could not summon the energy for a late rally and the points deservedly went back to Glasgow.