Stephen Eustaquio scored a dramatic stoppage-time winner as co-host Canada edged South Africa 1-0 in the Los Angeles suburb of Inglewood on Sunday, advancing to the last 16 at the FIFA World Cup as the knockout phase got underway at the tournament in North America.

With both sides making their maiden appearances beyond the group stage at international football's global showpiece, a tense round of 32 clash appeared to be heading for extra time, before Eustaquio broke South African hearts with a clinical strike from just outside the box in the 92nd minute.

The Porto midfielder, who has been on loan at LAFC, controlled the ball with his chest prior to unleashing a shot that sailed past Bafana Bafana goalkeeper Ronwen Williams and found the bottom corner.

That settled a contest which featured few clear chances, with the Canadian bench streaming onto the pitch as the majority of the fans erupted in celebration of a historic victory.

"We are excited that we're still playing, relieved that we managed to get over the line. It was a difficult match, we knew it was going to be," said Canada's Alistair Johnston. "It's still a pinch-me moment, honestly, we just won a knockout-round match at a World Cup."

Les Rouges were appearing in the knockout phase for the very first time, but their joy over achieving the feat was tempered by the fact that they finished second behind Switzerland in Group B.

That meant the Canadians had to head to the United States for this match, rather than staying home in Vancouver. And now they will travel to Houston for a round of 16 match on Saturday against the winner of Monday's match between the Netherlands and Morocco.