The massive score was too much for England, who had posted 385 in the first innings, before falling for 240 in the second dig, unable to force the Proteas to bat again.
The victory ends South Africa’s winless run at the Oval which dated back 11 matches, while it boosts their hopes of becoming the number one ranked Test nation.
Skipper Smith was proud of his side but looked ahead to the Second Test in Leeds.
“It’s an extremely proud moment for all of us in our team,” he said. “We are going to Headingley and the conditions will be very different and we understand it will be a very different Test match.”
England skipper Andrew Strauss said: “We were outplayed in the last four days of the game. We set the game up well on the first day. South Africa used the conditions to their advantage on day two and they never let us back into the game.”