The awards ceremony was held at the PSL offices in Parktown on Wednesday afternoon.
It was the second time this season that Tau and Mosimane won the awards.
In January, the duo were announced as the winners for December.
Tau, who has been in scintillating form for Sundowns during the course of the season, played a vital role for his title-winning side during April as he scored two goals and provided three assists. The champions profited immensely from the forward’s great contribution in attack which eventually saw Sundowns over the line by the end pf the month.
To win the award, Tau overcame his competitors such as Musa Nyatama of Orlando Pirates, Maritzburg United midfield due of Fortune Makaringe and Lebohang Maboe and club teammate Wayne Arendse.
Pitso, on the other hand beat off competition from coaches who also did well during the period such as Fadlu Davids, Micho Sredojevic and Luc Eymael.
The judges were impressed by the manner in which the Soweto-born coach managed his team selection and rotation policy during a tough period where the club was faced with other critical cup competitions and still went unbeaten in the league.
He was praised for his tactical acumen and grinding out results during tough outings on their way to winning their record 8th Absa Premiership title.
Orlando Pirates midfielder Musa Nyatama and coach Milutin Sredojevic won the awards for March.