A first-half try by captain Siviwe Soyizwapi was added to after the interval by Chris Dry and replacement Seabelo Senatla. None were converted.
"We call ourselves a defence team, and we're proud of it,” Soyizwapi said.
Having won Dubai for a record seventh time, and fourth time in the last six tournaments, South Africa goes to its home Cape Town Sevens next weekend leading a world sevens series it last won in 2018.
“The rust is off and we're keen to play at home,” Soyizwapi said.
Both finalists had scares in the knockout stages. South Africa scored two first-half tries then hung on to beat Argentina 12-5 in the quarterfinals, while New Zealand beat England 19-12 in the semifinals with a last-minute try by Salesi Rayasi.
Meanwhile, the New Zealand women won consecutive Dubai titles after beating Canada 17-14 in their final.