The win moves Dikwena up to 12th place on the log, while the defeat for AmaTuks leaves them in seventh spot.
Allan Freese’s men dominated the early exchanges on what was a windy evening in the South African capital.
The best chance of the opening 45 fell to Ndumiso Mabena in the fifth minute. The former Orlando Pirates man looked sure to score, but Washington Arubi and then Siyabonga Shoyisa were on hand to keep the striker's close-range effort from crossing the line.
Dikwena continued to enjoy the upper hand, with Vuyo Mere guiding his free-kick attempt inches wide of Arubi's left hand upright soon after.
AmaTuks hardly saw the ball in the first-half, but to their credit they were keeping Dikwena at bay with Stars launching attack after attack.
The Phokeng-based side failed to turn possession into goals with the score deadlocked at 0-0 at the halfway mark.
Mpho Matsi went close for the hosts in the 67th minute. A header clearance fell to the holding midfielder, whose half volley from way out flew just wide.
Stars continued to look the more likely to open the scoring, though, and did just that with three minutes of regulation time remaining.
Rodgers latched onto Tintswalo Tshabalala's pin-point cross for his eighth goal in all competitions.