Zimbabwean striker Kingston Nkhatha netted his first goal since October early on after receiving a pass from defender Clayton Daniels.
United, who climbed to ninth in the standings with the win, replaced coach Igesund in midweek with former Kaizer Chiefs mentor Stuart Baxter.
Stars are eighth on the table with 21 points from 15 games.
SuperSport took the lead in the 15th minute when Nkhatha fired home a low shot past Daouda Diakite.
Stars’ best chance of the half fell to Danny Venter soon after, the attacker unlucky to see his attempt cleared off the line by Dean Furman, who got back well to assist his goalkeeper.
The visitors should have pulled level four minutes into the second stanza, but Makhehleni Makhaula was unable to keep his cool in front of goal after bursting into the penalty area.
SuperSport were unfortunate not to double their lead on 50 minutes after new signing Mark Mayambela's shot deflected onto the crossbar before Justice Chabalala hacked clear with Jeremy Brockie lurking.
Stars pressed forward for an equaliser, but SuperSport defended desperately in the latter stages to avoid a hat-trick of losses in the Absa Premiership.