The Urban Warriors have endured a tough start to the season, having failed to win their opening three games, which included a 1-0 loss to Orlando Pirates on Tuesday evening.
The poor start had seen Stanley Menzo's charges drop to 15th place in the Absa Premiership standings.
Polokwane were also searching for a return to winning ways after they lost 2-1 to Bloemfontein Celtic
Ajax had an early chance take the lead after seven minutes but George Chigova produced a good save to deny Innocent Nemukondeni from the edge of the box.
The Urban Warriors enjoyed a good spell of possession in the early stages, although they could only test Chigova with strikes from distance.
Chigova proved to be the busier of the goalkeepers and showed his worth after 28 minutes by producing a fine save to deny Nemukondeni once again.
Rise and Shine had to wait until the 41st minute for their first opening but Walter Musona fired wide with only Brandon Petersen to beat.
Nevertheless, the score remained goalless as the sides entered the halftime break.
Rodney Ramagalela threatened early in the second half, but his shot from the edge on the box was turned away by Petersen in the 52nd minute.
Menzo opted for his first change five minutes later by handing a debut to Nigerian winger Ejike Uzoenyi, who recently received his work permit following his signing in early August.
The change paid off for Ajax as Uzoenyi's cross was fumbled by Chigova and Nxumalo was on hand to tap home in the 70th minute.
Polokwane responded with a double change on 80 minutes as Rendani Ndou and Vusimuzi Mngomezulu were introduced.
However, Nxumalo sealed the win for the Urban Warriors as he headed home Roderick Kabwe's cross for his second of the game.