The former Scunthorpe striker slotted home into the bottom corner after 12 minutes to secure all three points for Neil Lennon's side as they kept pace at the top of the table
The former Scunthorpe striker finished well into the far corner to ensure Neil Lennon's side would pick up all three points and make it five wins on the bounce.
Despite recently extending his contract at Celtic Park until 2015, captain Scott Brown was left on the bench by Lennon for their trip to Tannadice, while Wales international Joe Ledley was ruled out with an ankle injury.
In-form striker Hooper returned to the side in place of Ki Sung-Yueng and opponents United stuck with the same starting XI that drew 0-0 with Motherwell last week.
Celtic came close to opening the scoring after just six minutes as Anthony Stokes headed over the top from a James Forrest cross.
They would, however, take the lead in just the 12th minute as Hooper scored his 11th SPL goal of the season, slotting the ball into the far corner after being supplied by Forrest.
Scotland international Forrest then had a chance to put the visitors two in front after combining well with Stokes, but his effort was saved by United stopper Dusan Pernis as Celtic looked to turn their domination into goals.
The visiting side continued to dominate the possession stats in the second half without creating too many clear-cut chances.
Former Celtic man Willo Flood struck over the top before Forrest came close again at the other end but couldn't trouble United keeper Pernis.
The missed chances would not cost Lennon's side, though, as they held out to secure a vital three points in the SPL title race and move to within four points of current leaders Rangers.