Head coach Desiree Ellis made five changes to the team that drew 0-0 against Slovakia in the opening match, and the move paid dividends.
Banyana Banyana looked fresh and had free flowing movements.
Roxanne Barker came in for Andile Dlamini in goal, while Rachel Sebati, Kgaelebane Mohlakoana, Melinda Kgadiete and Sduduzo Dlamini replaced Linda Motlhalo, Leandra Smeda, Jermaine Seoposenwe and Chantelle Esau respectively.
Mohlakoana made Banyana Banyana’s intention very clear early in the first half when she sent in a fierce shot, but it went wide of Hungary’s goal.
Lebohang Ramalepe was the next to test the opposition goalkeeper, but her shot was saved.
Hungary also fired a veracious shot at Barker, but found her alert.
However, there was no denying Thembi Kgatlana in the 21st minute.
She was set free with a delightful pass, leaving her marker for dead before slotting the ball past the advancing Biro Barbara in the Hungary goal to give Banyana Banyana a 1-0 lead going into the break.
South Africa suffered a setback when Dlamini was stretchered off the pitch after being fouled in the 51st minute. Her place was taken by Esau.
Sensing defeat, the Europeans sent everyone into attack. They were almost rewarded when their strike hit the crossbar, and the ball was cleared, helping Banyana Banyana survive.
South Africa made another forced substitution when Kgatlana had to leave the field injured and Smeda took her place.
It was then end to end stuff, with both teams attacking each without creating any clear-cut chance.
In the end, South Africa got their first three points of the tournament – to leave them second in the group with four points.
In the other clash played earlier in the day, Korea DPR defeated Slovakia 1-0 to take control of Group C. The Asians are now on six points after two rounds of matches.
Banyana Banyana’s third and final group stage match will be against Korea DPR on Monday, March 5. Kickoff is at 13h00.
Hungary will face Slovakia in the later kickoff at 18h00.