In a dull opening period, chances were few and far between as both sides battled to retain possession.
The first shot on goal only came in the 19th minute as Celtic’s Frank Mhango fired a long-range effort inches over the crossbar.
Ten minutes later Stars had their first attempt on goal when Issa Sarr met a corner, but he headed wide from close range.
The best chance of the stanza fell two minutes before the restart, as Celtic goalkeeper Patrick Tignyemb had to produce a fine reflex save to prevent an own goal from his teammate Alfred Ndengane.
Phunya Sele Sele then broke the deadlock just shy of the hour-mark, as Mogorosi turned home a Lerato Lamola left-wing cross from 10 yards out.
Tumelo Mogapi missed a guilt-edged chance to double his side’s advantage in the 71st minute, as he failed to beat Dikwena's Siyabonga Mpontshane from a one-on-one situation.
Ernst Middendorp's men, however, managed to protect their slender lead to claim the spoils and go above their opponents into eighth spot in the standings.