Pakistan, the runners-up at the 2007 championship, had been defeated by England in their opening match and needed to beat the Netherlands.
Younus Khan's men survived in style with an 82-run win at Lord's to complete the second round Super Eights line-up.
South Africa, meanwhile, pulled off a one-run win off the last ball against fellow qualifiers New Zealand having made just 128-7.
Leg-spinner Shahid Afridi took four wickets for 11 - the fourth best return in all Twenty20 internationals - to star for Pakistan in their crucial Group B clash.
The Dutch, shock four-wicket winners over England in Friday's tournament opener and with a better run-rate at the start, were chasing 176 but needed to make only 151 to deny Pakistan the minimum 25-run margin of victory required.
But Afridi, well supported by fellow spinner Saeed Ajmal (three for 20), sparked a collapse that saw the Dutch decline from 42 for one to 93 all out.
Pakistan wicket-keeper Kamran Akmal, who also made four stump