Player of the match-winning performance from Kamran Ghulam (63 off 32 balls) took the score to 329.
Heinrich Klaasen made 97 for South Africa but the hosts were bowled out for 248.
Fast bowlers Shaheen Afridi (four for 47) and Naseem Shah (three for 37) were the main destroyers.
The win gave Pakistan an unbeatable 2-0 lead in the three-match series.
It was their fifth successive series win – and the third for the Champions Trophy hosts in the southern hemisphere season, following victories in Australia and Zimbabwe.
“It’s a team game, from beginning to end all of the guys are involved and contributing,” said Rizwan.
Babar and Rizwan, whose combined 204 one-day caps exceeded the total of the rest of the team, batted soundly and sensibly before Babar was out with a total of 192 in the 33rd over.
Rizwan followed three overs later with a sensational diving catch off his own bowling by 18-year-old one-day debutant Kwena Maphaka.
But the stage had been set for some power hitting by the batsmen who followed, notably player of the match Kamran Ghulam, who hit five sixes in making 63 off 32 balls.
With a licence to go for their shots, Pakistan scored 161 runs in the last 17 overs while losing their remaining six wickets.
“Me and Babar started slowly. We were looking for 300 but we got 320-plus. I have never seen Kamran Ghulam play an innings like that,” said Rizwan.
Left-arm fast-bowler Maphaka took heavy punishment but picked up four wickets while conceding 72 runs.
South Africa scored more briskly than Pakistan for most of their innings but although all of their first six batsmen made starts, only Klaasen made a significant score.
Klaasen, who made 86 in a losing cause in the first match in Paarl on Tuesday, hit eight fours and four sixes off 74 balls. He was the last man out, caught on the deep midwicket boundary.