Tshepo Ramaele, Lucky Khumalo, Tlou Masegela and Tommy Mandlazi returned for Tshakhuma introduced, while Chumani Bustaka was the only alteration for the Cape Town outfit.
Following an exciting opening, Tshakhuma drew first blood 11 minutes in after Thembisani Nevhulamba volleyed into the near corner following a ball from the right-hand side.
Ajax looked for a quick response at the midway point after a floating ball from the right found Rodgers who forced Ramaele into a one-handed save with a towering header.
A change for Ajax eight minutes to halftime saw academy graduate Dale Wakefield make his professional debut after replacing Sonwabile Mfecane.
Tshakhuma nearly went two goals up on 41 minutes after Molibedi Mokoena flashed the post following a low shot, while Naeem Amoojee stung the gloves of Nick Hengelman later on.
The Urban Warriors were out guns blazing in the second half and drew level after 47 minutes as Siphesihle Mkhize tapped home a goal-mouth after a scramble in the box.
Tshakhuma succumbed to a second goal three minutes later when Rodgers reacted first to a near post delivery before nestling the near corner of the net with a first-time finish.
Rodgers completed his brace inside 53 minutes after arriving unmarked at the back post to tap home a surging ball from Cohen Stander.
Ajax did not take the foot of the accelerator as Butsaka brought down a telling delivery from Wakefield on 60 minutes before drilling past Ramaele to extend the advantage.
Tshakhuma’ misery was further compounded after Lebohang Mabotja handled Butsaka’s cross to give away a penalty four minutes later, allowing Rodgers to complete his hat-trick.
The hosts looked for a second in the remaining minutes, but Hengelman scrambled a snap effort to safety after a ball from the right as Ajax revived their promotion chances and ended Tshakhuma’s in the process.
TTM: Ramaele, Mashele, Mabotja, Nyadombo, Thangwane, Amoojee, Mandlazi, Masegela, Khumalo, Mokoena, Nevhulamba.
Subs: Mamudzidi, Nhlapo, Makgoga, Moremedi, Dzaga, Hlongo, Mbandlwa, Ndebele, Makhubu.
Ajax: Hengelman, Johannes, Stander, Mukumela, Sibande, Mkhize, Kabwe, Margeman, S.Mfecane, Butsaka, Rodgers.
Subs: Leaner, Mahamutsa, Mokate, Velebayi, Wakefield, Siyasi, K.Mfecane, Koopstadt, Bakx.