After consecutive singles, South Africa needed seven runs to win from the final four deliveries.
After Brunt's caution with four balls remaining, South Africa's Mignon du Preez smashed a six followed by another boundary to win her team the game with two balls to spare.
In reply to England's 8-123, South Africa needed 21 off the last 13 balls to snatch victory.
Du Preez was dropped on two, and she made the most of the chance in her 100th T20 international.
She finished unbeaten on 18 off 11 balls, with her match-winning shot sparking wild celebrations.
Dane van Niekerk (46 off 51 balls) and Marizanne Kapp (38 off 33) played crucial roles in setting up South Africa's innings.
However, it was Brunt's tough decision that had the cricket world talking after the match.
Brunt was herself given a warning while batting in England's innings.
In the 17th over, as England's innings struggled to click into gear, Ayabonga Khaka pulled out of her delivery stride after Brunt had walked over the crease while backing up in expectation of a quick single.
Khaka's sportsmanship paid off handsomely for the South Africans when Brunt returned the favour in the dramatic final over.
Cricket commentators around the world have responded to the controversial moment by both applauding Brunt's display of sportsmanship and deriding her for failing to capture the dismissal.
The so-called Mankad dismissal, named after Indian cricketer Vinoo Mankad who famously executed a non-striker run out while bowling during a 1947 test tour of Australia, is a perfectly legitimate dismissal under Marylebone Cricket Club Law 41.16.
"If the non-striker is out of his/her ground at any time from the moment the ball comes into play until the instant when the bowler would normally have been expected to release the ball, the non-striker is liable to be run out," the law states.
"In these circumstances, the non-striker will be out run out if he/she is out of his/her ground when his/her wicket is put down by the bowler throwing the ball at the stumps or by the bowler's hand holding the ball, whether or not the ball is subsequently delivered."
The win was also sweet revenge for South Africa, who lost to England in the semi-final of the 2017 one-day World Cup.
"We kind of had a monkey on our back — it's now done and dusted," du Preez said of turning the tables on England.
"There has been a few nightmares in the past (against England) but to finally put that behind us and to move forward is really exciting.
"We said this year we want to go one step further than the semi-finals and take the World Cup trophy home."
England will probably have to win their remaining three group games — against Thailand, West Indies, and Pakistan — in order to reach the semi-finals.
"It puts the pressure on, doesn't it," England batter Natalie Sciver said.
"In terms of our team, a bit of pressure will hopefully see the best of us. "Hopefully we can go out there and play positively and play with freedom.
"I know the first game you sometimes have a few nerves around. I was nervous since two days ago watching the first game. Nerves can be good, but they can also be bad sometimes."
