Matsatsantsa had gone nine matches unbeaten in the Premiership prior to their trip to Bloemfontein, but goals from Joel Mogorosi and Ruzaigh Gamildien took Phunya Sele Sele to a deserved victory.
Celtic were the first to threaten a goal, with Thabo Nthethe getting on the end of Lyle Lakay's seventh-minute corner kick and directing a header on target, but United goalkeeper Ronwen Williams parried the ball away to safety.
Phunya Sele Sele broke the deadlock with their second attempt on target. On 26 minutes Gamildien drove in a lofted cross from the right flank and Mogorosi finished off from close-range after a fumble from Williams to make it 1-0 to the home side.
Matsatsantsa responded with a couple of corner kicks as they looked to build pressure and come up with a replay before the half time break, but Celtic were able to protect their lead up to the interval and almost doubled it when Gamildien struck a shot direct from a free kick just over the bar on 44 minutes.
The visitors made a double substitution early in the second half, with coach Gavin Hunt throwing on Sibusiso Zuma and George Maluleka in place of Ashley Hartog and Clifford Mulenga respectively.
However, it was the hosts who scored next and extended their lead to 2-0. On 58 minutes Gamildien added to what was already a fine personal performance with a long-range strike that had the beating of Williams and found the back of the net.
The visitors pulled a goal back on 89 minutes when Zuma beat goalkeeper Patrick Tignyemb with an 18-yard shot, but Celtic were able to hold out for the victory and secured three important points in their quest to cement a top half finish.