The first chance of the game fell to Jason Denayer as early as the third minute, but his right-footed shot from the centre of the box was saved.
Leigh Griffiths came close just minutes before, before Kris Commons and Virgil van Dijk tried their luck but in vain.
Celtic finally got the breakthrough in the 28th minute when Commons fired home from close range.
Efe Ambrose could have doubled the Bhoys’ lead just two minutes later had his header from close range been on target.
Commons had two good chances before the end of the first half, before Mario Bilate came close for United in the opening minutes of the second period.
However, Celtic soon regained authority of the match following the sending-off of United defender Sean Dillon, with Stefan Johansen, Griffiths, Denayer and Anthony Stokes all going close.
Then with 12 minutes of normal time remaining, James Forrest ended the game as a contest with a long-range effort after being teed up by John Guidetti.
Forrest had a great chance to make it 3-0 to Celtic in the final minutes of the encounter, but his penalty was saved.