However upon seeing his second-string side slip behind 10-7 early in the second half, White made sweeping changes by bringing on his entire bench including full-back Percy Montgomery who earned a record-breaking 90th cap.
South Africa did manage to score four tries to make sure of a bonus point which guaranteed top spot in Pool A and a quarter-final tie, most likely against Wales, in Marseille on October 7.
Tonga went ahead after nine minutes when Pierre Hola kicked a penalty awarded for offside before Andre Pretorius, South Africa fly-half, missed two penalties of his own.
However the Springboks scored the first try of the match in the 18th minute when Tonga were caught napping after being penalised for not staying on their feet, with fullback Ruan Pienaar taking a quick tap and scooting over with Pretorius adding the extras to make the score 7-3 at the break.
Tonga spectacularly stormed to the lead four minutes after the interval when prop Kisi Pulu was driven over and Hola added the conversion to make the score 10-7, prompting White to make five changes, bringing on regular skipper Jon Smit, Brendan Botha, Victor Matfield, Bryan Habana and Francois Steyn.
However Pretorius's miserable afternoon continued when he missed his fourth penalty kick before flanker Danie Rossouw was stretchered off with his neck in a brace.
Steyn took over kicking duties and he brought South Africa level at 10-10, before Juan Smith, who had replaced Rossouw, then eased Springboks nerves with his side's second try in the 59th minute with Montgomery, who had come on for the hapless Pretorius and passed Joost van der Westhuizen's mark of 89 caps, kicking the conversion for 17-10.
Bobby Skinstad, stand-in skipper, scored to make it 22-10 and Pienaar then finished off a sweeping move to make it 27-10 with South Africa looking like running away with the match.
South Africa were reduced to 13 men at one stage with both Steyn and Habana sin-binned while Tonga winger Joseph Vaka was also yellow-carded.
In a breath-taking finish, centre Sukanaivalu Hufanga reduced the deficit with a try in the corner before the islanders stunned South Africa with another try from lock Vilamai Vaki who won a sprint to the line in a move which started deep in their own territory from a Hola crossfield kick.
Hola kicked the conversion to make the score 27-22.
Montgomery then calmed his team's nerves with a penalty for Tonga collapsing the maul to edge his side to 30-22 before Hola kicked another penalty to secure a bonus point for his side, before they left the field to a standing ovation.