Robert Koren scored a late goal yesterday to give Slovenia a 1-0 win over 10-man Algeria in the teams’ opener, putting the Cup’s smallest nation — population 2 million, about the size of Houston — ahead of the United States and England in Group C.

On Friday, Slovenia faces the US, while Algeria takes on England.

Koren, the Slovenian captain, struck a long-range shot that Algeria goalkeeper Fawzi Chaouchi misjudged and allowed to bounce into the net off his arm in the 79th minute.

“I was just lucky to see it go in like that,’’ Koren said.

Algerian coach Rabah Saadane said the new World Cup ball was a challenge for goalkeepers.

“Everyone saw what happened with the ball, and what happened [Saturday] with England’s goalkeeper,’’ Saadane said. “You have to adjust to the flight of the ball.’’

Both sides knew they were heading into a match in which a loss would be costly, with England and the United States — both higher ranked — left on the schedule. The Group C favorites tied, 1-1, Saturday after a blunder by England goalkeeper Robert Green allowed Clint Dempsey’s shot to trickle into the net.

Algeria substitute Abdelkader Ghezzal was ejected in the 72d minute, picking up a second yellow card for handling the ball inside the Slovenian penalty area.

It was the first Cup victory for Slovenia. The Balkan country lost all three group matches in 2002.

“It was a mental victory,’’ said Slovenian coach Matjaz Kek. “We wanted to win so much, so it’s great for our confidence to get that win.’’

Algeria twice came close to scoring in the first half, when Nadir Belhadj’s 25-yard free kick forced Slovenia goalkeeper Samir Handanovic to stretch and push the ball over the crossbar, and when defender Rafik Halliche headed the ball just wide.

Saadane said Chaouchi apologized to the team for failing to track Koren’s shot. But the coach refused to criticize the goalkeeper.

“We must recover and prepare for an even more difficult match against England, which is the best of the group,’’ Saadane said. “It’s going to be very difficult now. We had a great opportunity today and we missed it.’’

The players seemed nervous in the first half, frequently losing possession with inaccurate passes and crosses.

Slovenia’s only scoring chance before the break was Valter Birsa’s long-range attempt in the 43d minute, tipped over the bar with a spectacular righthand save by Chaouchi.

The match could have taken a different turn 2 minutes before Koren’s winner when Algeria’s Karim Ziani caught defender Marko Suler off guard and pushed toward the goal, but was cut off by Handanovic.