With time up, Frawley kicked his second drop-goal of the game on Saturday to hand the tourists their second ever win away in South Africa and complete a famous victory after they had lost the first Test 27-20.
Ireland held a deserved 16-6 lead at halftime thanks to the only try of the game from halfback Conor Murray, but faced a resurgent home team in the second period and were forced into numerous errors by Springbok pressure.
South Africa fly-half Handre Pollard kicked eight penalties as the hosts looked to have wrestled the initiative in the contest, before Frawley's pressure kick snatched victory for Ireland.
"It was a proper Test match that," Ireland captain Caelan Doris said. "We were pleased with how we began, but credit to the Springboks, they showed their class to turn it around and get up by four points.
"It was back and forth after that but I was just elated to see the ball sail through the posts at the end there.
"We had to just keep believing, we knew if we got down there into the Springbok 22, we could score. It is a good feeling to end a long season with a win like that."
The physicality of the contest was brutal at times with Ireland initially winning the battle, before the Springboks roared back in the second half.
Trailing by five points with 10 minutes to play, Frawley kicked the first of his drop-goals to move his side within striking distance, before completing the job in the final play.
Ireland were the better side in the first half and scored a superb try their early pressure deserved. Fullback Jamie Osborne got through the tightest of gaps and fed centre Robbie Henshaw, who slipped a pass back inside to Murray to score.
The Springboks set a marker when they won a scrum penalty to reduce the deficit, but there was a contrast between Ireland's slick attack and the home side, who knocked on when well placed on several occasions.
Two Pollard penalties reduced the deficit to four points in the second half, the second of those awarded when Doris was yellow carded for a dangerous clear-out at the ruck and the visitors were reduced to 14 players for 10 minutes.
The Springboks' pressure was relentless after that and forced Ireland to continue to give away penalties. When Pollard added a sixth, the home side led for the first time after 56 minutes.
They extended their lead on the scoreboard to four, only for Frawley's two pieces of brilliance to send the visitors home victorious.
"We weren't as intense as we were last week in the first half," Springbok captain Siya Kolisi said. "We did well to fight back, the guys on the bench came on and made an impact.
"Ireland had the upper hand and physically, they dominated us in the first half. Last week we set the tone, this week they did and well done to them."
