Pakistan rode Babar's 68 off 46 balls to reach 6-140 in 19 overs in Lahore on Saturday, running down South Africa's 9-139 after with visitors lost the toss and were asked to bat first.
An inexperienced South Africa won the opening game by 55 runs at Rawalpindi before Pakistan made a strong comeback with back-to-back comprehensive wins to clinch the series 2-1.
Babar controlled the chase well after left-handed opener Saim Ayub was out for his fifth duck in his last 10 T20 innings.
The selectors had ignored Babar for almost a year before recalling him for the series against the Proteas as Pakistan still search for the right batting combination for next year's T20 World Cup.
He made a duck in the first match, but overtook Rohit Sharma's record for most runs in T20s when he made 11 not out in the second.
Babar started off cautiously against the left-arm spin of George Linde, but grew in confidence against the pace with bowlers finding it difficult to hit the right lengths with the wet ball because of heavy dew.
He shared a match-winning 76-run stand with captain Salman Ali Agha (33) as South Africa struggled to get the breakthrough.
Babar brought the capacity crowd of over 32,000 on their feet at the Gaddafi Stadium when he reached his 50 with three successive boundaries against fast bowler Ottneil Baartman as Pakistan's premier batter pushed the scoring rate with shots on both sides of the wicket.
Pakistan had a minor collapse and lost four wickets for 14 runs with Agha chipping an easy catch in the covers and Babar departing when only 15 runs were required for victory as he pulled Bosch's short ball to Reeza Hendricks at deep backward square leg.
Lizaad Williams (2-26) and Andile Simelane (1-23), two of the three changes South Africa made from the team that lost the second game, picked up late wickets but by that time Babar's knock had sealed the game.
"This innings was long due. I backed myself, the team believed in me," Babar said.
"I was hoping for such a knock. … It is about how you absorb pressure. I wanted to do what the team needed, play according to the situation."
In South Africa's knock, Shaheen Shah Afridi (3-26), who was rested for the second game, picked up the wickets of Quinton de Kock and Lhuan-dre Pretorius before the Proteas had scored in the first over.
Another left-arm fast bowler, Salman Mirza, also bowled to tight lengths in the power play and didn't allow Reeza Hendricks (34) and Dewald Brevis (21) to score freely.
Mystery off-spinner Usman Tariq (2-26) impressed in his debut T20 when he had Brevis mistime a pull of his second ball and Matthew Breetzke was clean bowled by left-arm spinner Mohammad Nawaz.
Faheem Ashraf then picked up the wickets of Ferreira and Linde off successive balls and South Africa crumbled to 6-76 in the 12th over.
Bosch made an unbeaten 30 off 23 balls that featured two boundaries in the last over of the innings to give South Africa some hope.
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