Goals from Vusimuzi Mngomezulu and Rodney Ramagalela on either side of Goodman Dlamini's effort in the first half was enough to ensure victory for the visitors.
Mngomezulu opened the scoring after just 40 seconds from the kick-off.
Just after the half-hour mark, Thokozani Sekotlong squandered a chance to draw level as he sent the ball wide of the mark from a free-kick in a promising position.
The home side drew level seven minutes before half-time as Goodman Dlamini's floated header caught George Chigova off his line.
However, Rodney Ramagalela bagged his ninth league goal of the season as he fired City back into the lead in the 44th minute.
The visitors should have had a two-goal cushion 10 minutes into the second stanza, as Stars' defenders were adjudged to have cleared off the line but replays showed the ball crossed the line.
A mistake by Thela Ngobeni shortly after the hour-mark as Ramagalele stole possession in a threatening area but the keeper recovered to deny the attempt at goal.
Ngobeni then made an excellent reflex save in the 66th minute to deny Mngomezulu's effort from close range.
Anas had an opportunity to draw level at the other end but Chogova was up to the task he blocked th striker's effort from close range.
Vilakazi had a brilliant chance to get on the scoresheet with 15 minutes to go after good work down the right hand side had the midfielder in acres of space, but he blasted his shot wide of the target from 15 yards out.
Stars continued to torment the City defense in the final stages of the match, but Rise and Shine held firm to see out proceedings with the score in their advantage.
The result sees City consolidate their position in sixth, with 37 points from 26 game, while Ea Lla Koto are at risk of dropping into the relegation zone as 15th place Baroka have a game in hand against Bloemfontein Celtic on Sunday.