PORT ELIZABETH, South Africa — Substitute Mark Gonzalez headed in the only goal in the 75th minute today, giving Chile a 1-0 win over 10-man Switzerland at the World Cup.

Gonzalez headed in a pass from Esteban Paredes, who had rounded the Switzerland defense and crossed to Gonzalez at the back post.

“We had some good luck near the end when we got the goal,” Gonzalez said. “We just kept trying our best, trying hard, and we got the goal. This was a great moment for me and for our team.”

Switzerland played a man down from the 31st minute, when midfielder Valon Behrami was sent off with a straight red card for violent conduct.

Before Chile scored, Switzerland set a World Cup record in the 69th, going 551 consecutive minutes without conceding a goal. That broke the previous mark of 550 held by Italy at the 1986 and 1990 tournaments.

Switzerland substitute Eren Derdiyok nearly equalized in the 90th but sent his shot wide as the Swiss put on late pressure.

The win gives Chile six points and first place in Group H. Switzerland, which upset European champion Spain 1-0 in its opening match, has three.

“We are in a good position, and we have one more game to prove ourselves even more,” Gonzalez said.

Chile had all the first-half pressure, even before Behrami’s sending-off, with four of nine shots on target, while Switzerland had none of its three shots on target.

Alexis Sanchez appeared to give Chile the lead in the 49th minute, but he was clearly offside. He nearly scored in the 55th on a clear break but was thwarted on the right side by Switzerland goalkeeper Diego Benaglio.

Chile included striker Humberto Suazo in its starting lineup, while Steven Von Bergen replaced injured defender Philippe Senderos for Switzerland. Senderos, who has an injured his right ankle, will also miss Switzerland’s final group match against Honduras at Bloemfontein.

Suazo was replaced by Jorge Valdivia to start the second half, and it was not immediately clear if Suazo had reinjured his ankle.

Chile midfielders Arturo Vidal and Carlos Carmona had back-to-back excellent chances from about 25 yards in the 10th minute, both blocked by Benaglio. Switzerland had no clear chances for much of the game.

It took an over-anxious Suazo only 90 seconds to be booked by Saudi Arabian referee Khalilk Al Ghamdia for a hard tackle. Blaise Nkufo of Switzerland and Carmona were booked a minute apart for challenges on each other.

It was Carmona’s second booking of the World Cup, meaning he will miss Chile’s final match against Spain on Friday in Pretoria.