It was Celtic's fifth SPL win in a row since Neil Lennon took over as interim boss and they were cheered off by the travelling fans at the end.
United substitute Genno Myrie-Williams saw red in what was a feisty encounter.
Hoops caretaker manager Neil Lennon claimed that his players had deserved better protection from the match officials.
“I saw a team out there, working hard for each other, brave in the challenge and hunting in packs,” he said. “Some of our play was magnificent but we were also gritty when we needed to be. We were good value for the win.
“There were eight yellow cards and one red but the referee should have stamped on that earlier. There was only one team trying to win the game and United were a bit crude at times but I’ve got to credit my boys for standing up to it because I told them not to be bullied.”
Understandably, Houston did not share that assessment. “We didn’t reach the standards we can today but we’ve been on an 11-game unbeaten run and reached the Scottish Cup final,” he said.
“We were still in the game until the final minute for all their supposedly free-flowing football. To say that we didn’t try to play football was wrong.”