It took some brilliance from the Sevens star to break the Fijian stronghold on the game, as the home side looked comfortable at the break, leading 10-5 and playing most of the rugby in the opening half.
Tshiremba opened the second half scoring as the Bok Women took a 12-10 lead, while a second try edged them into a 17-10 lead. Fiji kept coming back, but a third try in the 78th minute by the winger shut out the host team.
Fiji came out fast, with two early South African breakdown penalties handing the hosts momentum before wing Atelaite Buna scored in the left corner. The Bok Women were sloppy in possession, with handling errors disrupting their rhythm.
They soon turned to their powerful pack, and a dominant scrum earned a penalty and attacking lineout. Lindelwa Gwala crashed over from a superb drive to level the scores after 16 minutes.
Two yellow cards then put South Africa under pressure. Zintle Mpupha was binned for cynical play at the breakdown, allowing Adi Vani Buleki to score, before Anacadia Minnaar was also sent to the sin bin. Despite being reduced to 13 players, the visitors held firm to trail 10-5 at half-time.
The second half belonged to debutant Tshiremba. She opened her account after a fine break and pass from Maceala Samboya, with Byrhandre Dolf's conversion putting South Africa 12-10 ahead.
Tshiremba struck again after a wayward Fijian kick, racing clear to extend the lead to 17-10. Fiji hit back through Adi Salote Nailolo, before Vainah Ubisi restored South Africa's advantage with a maul try.
The hosts refused to go away, with Ivamere Rokowati's late try reducing the deficit to 24-22 with five minutes remaining. But after Fiji lost another player to the sin bin, Tshiremba completed her hat-trick from a series of attacking phases to seal the win.
Dolf's conversion was wide, but the damage was done and South Africa walked away series winners with their sixth win in seven matches.