Proteas captain Dane van Niekerk won the toss and opted to bat on a slow track at Sydney Showgrounds, with her team making a competitive 136 for six, boosted by Wolvaardt’s late fireworks.
In reply Pakistan, missing captain Bismah Maroof who was ruled out of the tournament on Saturday with a broken thumb, could only manage 119 for five.
South Africa have now won three from three in Group B — including a six-wicket humbling of England and a 113-run thumping of Thailand — to make only their second T20 semi-final following their efforts in 2014.
If England beat the West Indies later Sunday, they will join them in the last four.
“I’m really happy, but have to give credit to Pakistan, they gave it a massive go and kept coming at us,” said van Niekerk.
“It was an incredible game to be a part of,” she added, while paying tribute to Wolvaardt.
“It’s only her third time batting at five, she usually bats at the top, and to display her skills like that, she got us the winning total.”
The dangerous Lizelle Lee, who smashed a century in their last match against Thailand, immediately went on the attack as she opened the Proteas innings, crashing a four off the third delivery.
But pace spearhead Diana Baig bowled a beautiful outswinger and she got an edge to Sidra Nawaz behind the stumps in a big breakthrough for Pakistan.
Baig struck again with van Niekerk gone for three, dragging onto her wicket, to leave South Africa at 17 for two.
Mignon du Preez (17) and Marizanne Kapp (31) steaded the ship, then Wolvaardt, 20, played what proved to be a critical knock.
She carved out a high-quality unbeaten 53 from 36 balls, including fours off the final three deliveries.
Pakistan made a brisk start, whacking a quick 18 before Shabnim Ismail removed Muneeba Ali in a rare T20 wicket-maiden.
Omaima Sohail came to the crease but lasted just three balls before being run out in a comical mix-up with stand-in skipper Javeria Khan, then the dangerous Nida Dar departed for three.
A desperately unlucky Khan was batting beautifully in her 100th T20 when she was run out for 31, caught outside her crease when Aliya Riaz drove the ball back at bowler Chloe Tryon who got a hand on it and it rolled onto the stumps.
Needing 58 off the last five overs, Aliya Riaz (39 not out) and Iram Javed (17 not out) did their best but were denied by tight bowling.
“I would say fielding and bowling was good for the first 16 overs and then we lost our way a bit,” said Khan.
“It was a slow wicket and we should have restricted them to under 120, If we’d done that, the game would have been different.”
