Chasing a Duckworth-Lewis revised target of 298 in 43 overs, the Brendan McCullum-led side rode on an unbeaten 84 from Grant Elliott to reach their target with a ball to spare.
"Big Congratulations to New Zealand for making the ICC World Cup finals and playing amazing cricket... #CWC15. Its tough to see a side lose in a match like the semis. Well played South Africa," Tendulkar tweeted.
"Elliot is spot on, amazing support for the NZ team from the start of the WC. They deserved this win for the positive approach #CWC2015.
"Bad luck SA. You can see how emotional they are and you feel for them. They wanted this desperately. They gave it all they had. #CWC2015," the spin great tweeted.
New Zealand will take on the winner of the second semi-final between India and Australia in Sydney on Thursday.