South Africa's bowler Morne Morkel, third left celebrates the dismissal of Zimbabwe's captain Brendan Taylor, unsees with his teammates, Jean-Paul Duminy, third trght and Robin Pietersen, second right during the ICC Twenty20 Cricket World Cup match between South Africa and Zimbabwe in Hambantota. AP photo
The 36-year-old allrounder grabbed 4-15 and was well supported by Morne Morkel's 2-16 as Zimbabwe
were kept down to 93-8 -- their second lowest total in all Twenty20 internationals -- after they were put into bat.
Openers Richard Levi then notched 50 not out and Hashim Amla an unbeaten 32 to knock off the low target in the 12.4 overs to cap a comfortable victory for one of the title favourites in this 12-team competition.
The defeat meant Zimbabwe becomes the first team to go out of the tournament after a one-sided match watched by just 1,000 fans in Mahinda Rajapaksa stadium.
Levi hit six boundaries off 43 balls, while Amla hit three off his 33 deliveries.
Earlier Zimbabwe failed against a ruthless South African pace quartet, led by Kallis and Morne Morkel.
Craig Ervine top-scored with 37, and added 35 for the fourth wicket with Stuart Matsikenyeri (11), to help Zimbabwe just avoid their lowest total of 84 in all Twenty20 internationals, made against New Zealand in 2010.
Morne Morkel dismissed Vusi Sibanda (nought) and Brendan Taylor (four) in his first two overs before Kallis polished off the middle-order with the wickets of Matsikenyeri and Elton Chigumbura off successive deliveries in his first over.
He then dismissed Graeme Cremer (six) and Ervine to improve on Morne Morkel's 4-17 against New Zealand in 2007 which was the previous best bowling by a South African in a Twenty20 match.
Hosts Sri Lanka, who beat Zimbabwe by 82 runs, play South Africa in the final Group C match on Saturday.
The top two teams from each of the four groups will advance to the Super Eights round.