Their vital eighth-wicket stand in their first ODI game lifted Pakistan out of serious trouble at 131-7 and ensured the tourists had something to bowl at. In the end it proved more than enough as only Kallis and JP Duminy (49) threatened.
Tailenders Dale Steyn (15) and Morne Morkel (17) launched South Africa's final attack, but Bhatti sent both packing and ended the game by rattling their stumps with perfect yorkers.
The second ODI is in Port Elizabeth on Wednesday.