The result at Beausejour Stadium also meant England progresses to the final four while South Africa exits the tournament.
Umar Akmal's blistering 51 off 33 balls led Pakistan to a total of 148-7 from their 20 overs. Akmal cracked two fours and four sixes to lift Pakistan from early trouble at 18-3.
Fast bowler Charl Langeveldt claimed 4-19 off his four overs.
South Africa stalled early in their run chase and could only manage 137-7. A.B. de Villiers topscored with 53 off 41 balls but he fell at a crucial stage to off-spinner Saeed Ajmal, who grabbed 4-26.
South Africa's pursuit was undermined by the early loss of both openers.
Herschelle Gibbs smacked Abdul Razzaq straight to midwicket with the score on 12, then captain Graeme Smith mis-hit left-arm spinner Abdur Rehman to mid-on to make it 23-2.
De Villiers and Kallis added 33 for the third wicket but the required run rate kept climbing.
Kallis spent 21 balls compiling 22 before he was Ajmal's first scalp, thanks to a brilliant catch at long-on from Umar Akmal.
De Villiers smacked Rehman's final over for 20 runs to revive South African hopes but Ajmal claimed his wicket in the next over to tilt the balance.
Johan Botha blasted 19 off eight balls in a late flourish that threatened to produce a miracle for the Proteas.
However, with 17 needed off the final over, Ajmal removed Botha and ensured that only ones and twos were on offer to the batsmen.
Earlier, Pakistan recovered from a difficult start after winning the toss choosing to bat.
Salman Butt miscued a pull off Dale Steyn, Khalid Latif lofted Jacques Kallis to mid-on and Mohammad Hafeez was LBW to Langeveldt.
But Umar Akmal anchored the Pakistan recovery with two half century partnerships, adding 51 from 36 balls with his older brother Kamran and then a further 61 off 33 balls with skipper Shahid Afridi.
Kamran Akmal hit three fours and two sixes in his 37 off 33 balls.
Afridi, who supplied 30 off 18 deliveries, blasted four fours and a six.
