England fashioned excellent early tries for Manu Tuilagi and Freddie Steward but four penalties for Handre Pollard kept South Africa within five points at the break.
The Springboks then took command, cashing in on a series of England penalties to kick their way into the lead.
A try for Raffie Quirke on a rare second-half England attack briefly restored the home lead but Makazole Mapimpi crossed for the visitors and Fran Steyne edged them ahead.
England mustered one more attack and earned a penalty on the 22 that Smith smashed over to make it three wins out of three in November.
Source:
Reuters/RNZ Pacific