Having lost 12-11 to England in their European tour opener a week ago, the Springboks looked set to come up short in a close encounter when they trailed by four points as the game moved into additional time.
Aphiwe Dyantyi was denied a potentially game-winning try on South Africa's left flank when the TMO adjudged the final pass to be forward, but a penalty in the build-up offered the visitor another chance.
The Springboks duly took it as their forwards put the French pack under immense pressure on the opposite side of the field, eventually allowing substitute Mbonambi to slide over.
The hooker's dramatic score capped an impressive turnaround by the Springboks, who had trailed 23-9 in the early stages of the second half.
Defeat will sting for Les Bleus, who started brightly and quickly took a 6-0 lead thanks to a pair of Baptiste Serin penalties.
The visitor responded with nine points from the reliable boot of Handre Pollard, but France levelled the game with a Camille Lopez drop goal before seizing control of proceedings with a 12-point burst either side of the interval.
An attacking line-out allowed hooker Guilhem Guirado to break down the blindside to score the game's opening try in the closing stages of a first half that saw the host side firmly on top.
Serin added the conversion and was also on target with the extras after Lopez's clever high kick was fumbled by Sbu Nkosi close to his own line, allowing Mathieu Bastareaud to force his way over from close range.
However, Nkosi quickly made amends for his error by scoring at the other end, touching down on the right-hand side as France was caught short of numbers.
Pollard's conversion attempt went over via a deflection off a post, though the fly-half needed no assistance with two successful penalty attempts to cut the gap down to a point with an hour gone.
Another successful kick from Serin after a late tackle by Faf de Klerk – who escaped any further punishment – extended France's advantage, yet Les Bleus were unable to cling on through to the final whistle.
Both Cheslin Kolbe and Dyantyi were denied tries by video footage - the former losing possession as he looked to ground the ball over the line after a pulsating run – but it proved to be third time lucky for South Africa when Mbonambi touched down, Pollard adding the conversion with the final kick of a pulsating contest in the French capital.