The champions responded well to losing an 11th minute goal to Tannadice midfielder Stuart Armstrong with efforts from Efe Ambrose, Kris Commons and Joe Ledley.
However, at 2-1, the visitors were handed the chance to draw level when referee Bobby Madden surprisingly pointed to the spot after Celtic defender Adam Matthews tackled Gary Mackay-Steven but Fraser Forster saved from United skipper Jon Daly.
Commons grabbed his second from the spot 10 minutes into the second half before Anthony Stokes notched a double to complete the rout, with Johnny Russell scoring late on for th Taysiders.
Following wins against Rangers and Hearts, former Celtic defender McNamara said: "I was disappointed with the goals we lost and they obviously got a lift from us missing the penalty.
"I thought their keeper had a few good saves but the goals we lost were soft."
