Sterling batting from captain AB de Villiers and strong bowling cemented South Africa's place in the final eight, against a nonthreatening UAE attack.
Shenwari, who had been positively pedestrian for his first 40 runs, was dismissed for 96 after leading his side's chase to 211 runs to victory.
The co-hosts dismissed England for 123 and roared to victory in a mere 12.2 overs, which has firmly placed them as the team to beat this World Cup.
UAE looked on course to record their first win over a test nation in their 20th official one-day international until Williams and Ervine intervened.
Maria Sharapova will advance to the semifinals in the Australian Open, but Rafael Nadal's hopes have been dashed by Roger Federer's conquerer.
The Springboks put a positive spin on their narrow defeat to the All Blacks in a bruising encounter on Saturday.
The All Blacks' victory over the Wallabies on Saturday ensured the Bledisloe Cup remains in New Zealand for the 12th successive year.
Blood was spilled and both teams had players sent from the field yet New Zealand's 29-15 victory over SA was based around a simple principle.
Serena Williams has recovered from a nasty fall and painful ankle injury to blast her way into the second round of the Australian Open.
Martin Guptill and Daniel Flynn battled hostile pace bowling to guide New Zealand to 65 for no loss at the close of play on the third day on Sunday.