Defender Rudy Isaacs scored game's only goal in the 24th minute, handing United their seventh League win and moving them to 24 points – well in the race for the Absa Premiership title as the competition takes a lengthy break due to the upcoming Africa Cup of Nations finals in Ghana.
Supersport started brightly and Daine Klate forced goalkeeper Shu-Aib Walters into a good save in the 10th minute after controlling a fine long pass, turning inside defender Cyrille Mubiala and shooting on goal with his right foot.
The young United winger had earlier rattled the crossbar with a glancing header but he was, as television replays suggested, incorrectly ruled offside.
Supersport took the lead midway through the first half when Isaacs rose highest to meet an Elias Pelembe free kick at the back post and powered his header past Walters.
Referee Paulo Marques turned down a strong penalty appeal from Celtic on the half hour mark when Isaacs brought down Ghanaian forward Mark Amofah from behind on the left edge of the 18-yard area.
Quite whether the tackle had taken place inside or outside the penalty area was made immaterial when the official failed to pull back play for what seemed a blatant foul.
Four minutes before the interval, Supersport so nearly took a two goal lead but a brave intervention from James Madidilani, who got his head in the way of Thabo September's powerful goal bound shot after Walters had made a hash of trying to collect a corner kick, kept the score down to 1-0 at half time.
The skilful Pelembe, who was giving Celtic fullback Didier Mbendje a torrid time, really came to life in the second half, and his surging run in the 62nd minute set up Katlego Mashego with a clear sight on goal, but the striker's low shot was well saved by Walters.
That, sadly, was the only notable highlight of a disappointing second half where the hosts struggled to recreate their earlier fluency, while 'keeper Denis Onyango was rarely called upon to do anything more than take a goal kick or clear a back pass.