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Parkes, who only became eligible to play for the Welsh on Friday, crossed over along with centre partner Scott Williams to help the home side to a 21-3 lead not long after the half-hour mark.
South Africa fought back to be 22-21 up thanks to tries from Warrick Gelant, Handre Pollard and Jesse Kriel. However, a Leigh Halfpenny penalty 13 minutes from time allowed Wales to regain the lead and see out the match with some tenacious defending.
Victory for Wales followed defeats over the past month at home by Australia and New Zealand and provides a fillip to their preparations for the 2019 Rugby World Cup.
Dan Biggar's brilliant kicks gave Warrant Gatland's side the perfect start, first setting up Williams with a cross field kick in the fifth minute and then shortly after assisting 30-year-old Parkes to dive over for a dream start to his Wales career.
South Africa scored their first points from a Pollard penalty in the 31st minute. However, fullback Andries Coetzee then had his clearing kick charged down, allowing Taulupe Faletau to pick up the loose ball and feed Parkes for his second try which gave Wales an 18-point lead.
A Bok counter attack from Dillon Leyds cut the deficit before half-time as Gelant chased down Kriel's kick for South Africa's first score.
After the break, Pollard finished off a direct approach from the forwards as they worked their way down towards the Welsh line but his resultant conversion attempt hit the upright.
In the 55th minute, more driving from the forwards set up the backs as Kriel burst through Halfpenny's tackle to go over. Pollard made no mistake with the conversion for a 22-21 lead.
But the hosts were allowed to regain the advantage when Pieter-Steph du Toit was penalised for not rolling away at a maul. Halfpenny easily slotted over as Wales held on for their third successive home win over the Springboks.
South Africa finished their month-long European tour with two wins and two losses, increasing speculation over the future of coach Allister Coetzee.