South Africa won the toss and elected to bowl first, restricting New Zealand to 175 for seven in their 20 overs on a good batting wicket.
Markram led the charge in response as South Africa eased to their victory target with 17 balls to spare in a commanding performance with bat and ball.
South Africa head the Group B standings with a perfect six points from three games, followed by New Zealand (4 points), United Arab Emirates (2), Afghanistan (0) and Canada (0).
If UAE fail to beat Afghanistan on Monday, South Africa will be assured of a place in the next stage.
New Zealand had a good run rate throughout their innings, but kept losing wickets, which meant they posted a below-par score.
They were 64-4 after 6.4 overs before innings top scorer Mark Chapman (48 runs from 26 balls) and Daryl Mitchell (32 from 24) put on 74 for the fifth wicket to steady the ship.
When the superb Marco Jansen (4-40) dismissed Chapman, New Zealand added only 37 runs in the final six overs. Though he failed to take a wicket, Kagiso Rabada also bowled with great control for figures of 0-27 in four overs.
South Africa got off to a rollicking start to their reply, scoring 82 runs in the first six overs to break the back of the chase and as long as they kept wickets in hand after that, the rate would never be an issue.
Markram was superb at the top of the order as he reached his 50 from 19 balls, the joint quickest on the competition with Sri Lanka’s Dasun Shanaka against Oman.
He put on 62 for the opening wicket with Quinton de Kock (20 from 14) and carried his bat with an innings of power, placement and poise.
South Africa are next in action against the UAE in Delhi on Wednesday.
