Player of the match Beth Mooney's unbeaten 53-ball 74 did most to put the pressure on the South Africans in their first-ever World Cup final appearance on Sunday as the Australians, opting to bat, amassed 6-156 at Newlands.
Then Lanning's team bowled and fielded with clinical efficiency to always stay in control, as they ended up restricting the Proteas to 6-137 to lift the T20 global title for the third time in a row and the sixth time in the last seven editions.
Among a fine combined effort from the Australian bowlers, Megan Schutt, Ashleigh Gardner, who was voted player of the tournament, Darcie Brown and Jess Jonassen each took a key wicket as the Australians won a 13th world title in all in white-ball cricket.
The South Africans only ever threatened briefly with their opener Laura Wolvaardt cracking 61, but Schutt trapped her lbw in a key moment.
Mooney had kept the Australian innings ticking over but she scolded herself, fearing their total might not be enough.
"I was probably a little bit too hard on myself in the middle of that innings," said Mooney. "I walked off thinking we hadn't quite got enough on the board, but never judge a wicket until both sides have played.
"It was bloody tough out there but I think everybody did a great job."
Earlier, Gardner's 21-ball 29 also helped Australia overcame a slow start in the Cape Town showdown.
Mooney's quickfire 15-ball stand of 33 with Ellyse Perry (seven off 5 balls) ensured the defending champions scored 46 in the death overs despite Shabnim Ismail's double-wicket 20th over.
The 34-year-old South Africa quick became the leading wicket-taker in women's T20 World Cup history with her 42nd strike.
She was on a hat-trick when Tahlia McGrath took a single off the final ball as Australia finished on 6-156, leaving the match evenly poised.
Earlier, Gardner, promoted to Lanning's usual No.3 slot, marshalled Australia from 1-36 in the powerplay to double that run tally by the halfway mark.
Her 41-ball, 46-run second-wicket stand with Mooney, who played out a maiden in the sixth over against Ismail, broke upon the introduction of part-time spinner Chloe Tryon.
The left-armer had Gardner hole out to long-off, where South African captain Sune Luus completed a high catch without a hitch.
The allrounder then took a superb catch at deep midwicket off a Lanning pull to reduce the opposition to 4-122 with 17 balls left in the innings.
Australia amassed 34 off those 17, with Mooney, who brought up her second successive fifty of the World Cup, off 44 balls, alone fetching 25 in that tally.
Mooney's pivotal innings rescued Australia after her fellow opener, Alyssa Healy, scrapped to a 20-ball 18 that ended with a catch at cover off Marizanne Kapp.
