It was the second drop goal of the match by Frawley, a second-half replacement for fly-half Jack Crowley, as the visitors came from five points behind after leading 16-6 at half-time.
Ireland dominated the first half, but played second fiddle to the record four-time World Cup winners after the break and a string of Handre Pollard penalties put the Springboks 24-19 ahead.
A Frawley drop goal on 70 minutes narrowed the gap to two points before a capacity 52,000 crowd at Kings Park stadium in the Indian Ocean city.
The 26-year-old struck again in the final minute on just his sixth Test appearance after Ireland won a line-out, sending another drop goal between the posts in the enthralling clash of the top two ranked rugby union nations.
After referee Karl Dickson dismissed a claim of obstruction against Springbok winger Cheslin Kolbe, he blew for full-time, a week on from the hosts' 27-20 first Test win.
Ireland triumphed despite playing 10 minutes a man short after captain and No. 8 Caelan Doris was yellow carded on 48 minutes for foul play at a ruck.
In his absence, fly-half two-time World Cup winner Pollard kicked three of his eight penalties, turning a seven-point deficit into a two-point advantage.
In a reversal of the first Test in Pretoria, Ireland dominated from the kick-off and were rewarded after six minutes when Crowley kicked a penalty.
By then the Springboks had already been forced into a change with full-back Willie le Roux suffering concussion and one-cap Sacha Feinberg-Mngomezulu took his place.
Blood-covered face
South Africa lock Eben Etzebeth, his face covered in blood, was the next casualty, leaving the field temporarily with RG Snyman, who plays his club rugby in Ireland, coming on.
Ireland were dominating possession and territory and deservedly stretched the lead to 10 points with a try from scrum-half Conor Murray on 14 minutes which Crowley converted.
A break by full-back Jamie Osborne set up the score and centre Robbie Henshaw passed for Murray to race clear and score his 18th Test try.
Etzebeth returned only for fellow lock Franco Mostert to limp off and Snyman came off the bench again, this time permanently.
South Africa finally got on the scoreboard after 19 minutes when fly-half Handre Pollard, who missed three of seven kicks at goal last week, placed the ball between the posts.
When the world champions did get half chances they failed to take advantage with winger Kolbe knocking on and No. 8 Kwagga Smith dispossessed after charging down a Crowley clearance.
Pollard slotted another penalty, from a more challenging angle, on 35 minutes to cut the deficit to just four points, which flattered the home team.
But Ireland finished the first half strongly and two Crowley penalties from favourable positions gave them a 16-6 lead at half-time that they thoroughly deserved.
Whatever Springboks coach Rassie Erasmus said during the break had a massive impact as the home side took control and Pollard slotted six penalties while Crowley kicked just one for the Irish.
From 10 points behind, South Africa were five in front and then Frawley took centre stage with his drop goals turning the tide.
