The tourists were the more physical and clinical team and forced South Africa into a host of soft errors in the second test.
Wales, who at one stage were down to 13 men, scored three tries through centre Jamie Roberts, wing Alex Cuthbert and hooker Ken Owens. Flyhalf Dan Biggar converted those and added three penalties.
South Africa's points came through the two penalty tries and further scores from wing Cornal Hendricks and Willie Le Roux. Flyhalf Morne Steyn booted four conversions and a penalty.
Biggar opened the scoring with a penalty before Wales extended their advantage to 10 points when Roberts dived under the posts after Cuthbert had surged into a gap in the defence.
Three minutes later and the lead was stretched to 17-0 as Wales bulldozed close and Cuthbert finished off the move.
South Africa used their driving maul to good effect in the 38-16 first-test win in Durban and when they finally got into the Wales 22 just past the half-hour mark it proved a potent weapon again because they notched a penalty try.
The visitors then received two yellow cards in as many minutes, lock Luke Charteris and Biggar being sent to the sin-bin by referee Steve Walsh, both for collapsing a maul.
South Africa took advantage and centre JP Pietersen ran straight through the defence before passing inside to Le Roux who set up a score for Hendricks.
Steyn converted and the Welsh lead was down to 17-14 by halftime.
Restored to a full compliment of players early in the second period, a burst to the line by Owens was sent for a video review and although replays showed he grounded short and lost control of the ball, the touchdown stood.
Biggar booted two more penalties as Wales continued to pressure South Africa into mistakes to open a 13-point lead.
Hendricks then produced a fine break to set up a scoring chance for Le Roux after sustained home pressure.
Wales managed to keep the Springboks at bay until two minutes from the end when Hendricks burst down the right and, just as he was about to touch down, was barged into touch by fullback Liam Williams.
Another video review was called and it was ruled that Williams had not used his arms in the tackle, leading to the second penalty try and Steyn kicking the winning conversion.
