Tahir returned 4-53 from 10 overs against the country of his birth, helping to dismiss Pakistan for 191 in Wednesday's third one-day international in Abu Dhabi.
JP Duminy (64) and Faf du Plessis (55) had earlier set the platform for South Africa, whose 259-8 represented the highest score of the series so far.
South Africa captain AB de Villiers won the toss and elected to bat, with his side determined to respond to a heavy defeat on Friday.
Although they lost opener Hashim Amla (10) in the fifth over, young wicketkeeper Quinton de Kock (40) impressed.
De Kock hit five boundaries in his 57-ball stay at the crease and added 77 runs for the second wicket with du Plessis.
Although the former departed to Shahid Afridi (2-41 off 10), Duminy came in and picked up the slack.
The half-centurions batted very differently, with du Plessis hitting eight boundaries and Duminy, who turned the strike over with ease, just three.
De Villiers and David Miller struck 34 apiece in quick time to boost South Africa's cause.
Pakistan spinner Saeed Ajmal (2-38 off 10) bowled well but the likes of Mohammad Hafeez (0-45 off six) and Wahab Riaz (0-40 off six) leaked runs.
Although Mohammad Irfan (3-46 off 10) claimed the late wickets of Ryan McLaren (13) and Dale Steyn (two), South Africa's score looked imposing given the low totals previously posted in the series.
Pakistan's top five batsmen all reached double figures but failed to convert starts.
Opener Ahmed Shehzad hit seven fours in a 24-ball 32, setting the pace, before Steyn (1-31 off eight) removed the in-form batsman in the ninth over to leave the score reading 50-1.
That wicket slowed Pakistan's rate of progress and both Hafeez (15) and Umar Amin (13) followed Shehzad in departing when well set.
At 89-3, Pakistan were still in contention, but Tahir removed captain Misbah-ul-Haq (19), Umar Akmal (seven) and Asad Shafiq (11) to swing the match in South Africa's favour.
Despite impressive cameos from Wahab (33) and Sohail Tanvir (31), Pakistan's tail were ultimately left with too much to do as they fell well short of their target.