Benni McCarthy's charges have now moved to within one point of Mamelodi Sundowns, who lost to Polokwane City on Saturday afternoon.
Stars had a chance as early as the sixth minute when Bongi Ntuli fired just wide from close range.
Despite Stars' promising start, City enjoyed most of the possession in the opening 20 minutes of the first half.
Dikwena started seeing more of the ball after the 30-minute mark but they struggled to carve out any openings in the final third.
Roger de Sa's men ended did the half strongly but they were unable to break the deadlock as the sides went into the break level.
The Citizens pushed for an opening goal upon resumption of the second half and they went close in the 55th minute when Thamsanqa Mkhize hit the upright.
10 minutes later, the hosts went close to taking the lead when Robert Ng'ambi got on the end of Vuyo Mere's free-kick and sent a header just wide.
Manti Mekoa then came on for his Stars debut with just over 20 minutes remaining, replacing Lehlogonolo Masalesa.
However, it was the visitors who took the lead with eight minutes remaining when Roland Putsche finished off a well worked move to hand City the lead.
Dikwena threw numbers forward in search of an equaliser, but they were unable to bypass the City defence and the visitors walked away with three points.