Opting to bat, South Africa A rode on a fifty each from opener Sarel Erwee (75) and middle-order duo of Tony de Zorki (58) and Khaya Zondo (56).
While Saini took three for 42, fellow pacer Deepak Chahar claimed one for 35 and left-arm spinner Saurabh Kumar picked up two wickets.
Saini, who has been impressive in the series with seven wickets so far, gave India A an early breakthrough, dismissing rival skipper Malan (0) in the sixth over, while Saurabh sent back Zubayr Hamza (16) cheaply to reduce the home side to 44 for 2.
However, Erwee and Tony took South Africa A past the 150-mark before the latter was run out by substitute Upendra Yadav.
Saini then picked up two quick wickets, getting rid of Erwee and Senuram Muthusamy (0) to leave the hosts at 187 for 5 in 65.2 overs.
Khaya Zondo then took the onus and shared a fruitful partnership with Sinethamba Qeshile (22).
South Africa A 1st innings: 249 for 7 in 89 overs (S Erwee 75; Navdeep Saini 3/42).