Belgian striker Andrea Fileccia struck twice to go with a goal from Danny Venter as Stars claimed their first points of the season in their fourth game.
Middendorp, who left United on bad terms in June, replaced Kinnah Phiri in the Ea Lla Koto hotseat late last month.
The visitors started the better of the two teams and had the first shot on goal in the sixth minute when Nkosinathi Mthiyane fired a 20-yard free-kick just over the target.
In the 13th minute Chippa had another free-kick just outside the box, but this time Mark Mayambela shot wide of goal.
Seven minutes later Rhulani Manzini tried his luck from range, but he saw his effort well-saved by Stars goalkeeper Daouda Diakite.
In the 34th minute the home side took the lead against the run of play when a superb volley from Fileccia found the top corner of the goal.
Chippa almost equalised on the stroke of half-time when a 22-yard set-piece from Rhulani Manzini was magnificently saved by Diakite.
Stars almost doubled their lead three minutes into the second half when Fileccia’s effort from the edge of the box sailed inches wide of the post.
In the 64th minute Robert Sankara almost scored for the Ea Lla Koto when he met a Venter corner-kick, but his header skimmed the wrong side of the woodwork.
Thirteen minutes before the end of the match Venter made sure of the win for Stars when he found the back of the net with a clinical strike from just inside the box.
The icing on the cake was Fileccia’s second goal in the 84th minute when he turned home a pass from Venter to make it 3-0.