Lebogang Kukame, Moses Spandeel and Kleinbooi Taaibos scored for Phunya Sele Sele.
Celtic made their intentions clear from the start and deservedly went ahead in the seventh minute when Kukame capitalised on Thanda defender Bongani Mbele’s failure to clear a cross by Gary Goldstone, to score with a fierce shot into the roof of the net.
However, Celtic did not have things all their own way as Thanda came back strong, but their poor finishing cost them in the end, with Serge Djiehoua the main culprit.
The Ivorian should have leveled matters for Amabhubesi in the 36th minute when he rose unmarked to meet Mbele’s cross, but Djiehoua sent his close range effort straight at Celtic keeper Simon Gopane.
Thanda keeper Arni Arason ensured the scored remained 1-0 at the break with a superb save to deny Taaibos, from close range, in the 41st minute.
The second half was played at a frenetic pace with Thanda creating the first chance in the 59th minute when Djiehoua headed just wide from close range following a a cross from the left.
However, with the hosts pushing more men forward in search of an equaliser, they were always vulnerable to the quick counter-attack.
The visitors deservedly doubled their lead in the 66th minute when Spandeel scored with a volley from inside the area after the Thanda defence failed to clear a long throw-in by Celtic.
Taaibos secured the points for Celtic seven minutes from the end when he scored with a low shot following some woeful defending by Thanda Royal Zulu.
Thanda remain third from bottom on 24 points, and although Celtic are a place above them in the Absa Premiership, six points separate the two sides.