World Cup holders Spain survived a major scare before beating Colombia on penalties to reach the semi-finals of the Olympic women's football on Saturday, after the United States edged out Japan.

Ballon d'Or winner Aitana Bonmati converted the decisive kick in the shoot-out as Spain beat Colombia 4-2 on penalties after their quarter-final tie in Lyon had finished 2-2 at the end of extra time.

Spain now advance to a semi-final on Tuesday in Marseille against either hosts France or Brazil, who meet later.

Spain are going for gold in their first appearance in the Olympic women's football, but they were moments away from being eliminated after falling 2-0 behind to the South Americans.

Mayra Ramirez fired Colombia ahead early on and Leicy Santos doubled their lead early in the second half after a Linda Caicedo shot was saved.

Jennifer Hermoso pulled a goal back in the 79th minute for the world champions, who were then rescued when captain Irene Paredes turned in a Salma Paralluelo cross in the seventh minute of injury time.

That meant extra time, and no further goals led to penalties. Captain Catalina Usme's first kick for Colombia was saved, while Liana Salazar missed her attempt as Spain scored all four of their efforts from the spot to go through.

Earlier, Trinity Rodman scored a stunning goal in extra time as the United States edged Japan 1-0.

The daughter of former NBA superstar Dennis Rodman struck in stoppage time at the end of the first half of extra time to finally break the deadlock, and Japan's resistance, at a packed Parc des Princes in Paris.

That took the USA through to a semi-final on Tuesday in Lyon, where they will face either reigning Olympic champions Canada or 2016 gold medallists Germany.

  Rodman sinks Japan  

The USA remain on track under new English coach Emma Hayes to win a record-extending fifth women's football gold, and a first since defeating Japan in the London Olympic final in 2012.

That silver remains Japan's only medal in the competition and they go home after thwarting the USA for most of a tense quarter-final, where they failed to take what few chances came their way on the break.

"I honestly think that was the only way we were going to find a goal in that game," Rodman said of her moment of magic after she was set up by Crystal Dunn.

"Obviously we had tried all game long to get in between them and it wasn't working, but she played it in behind.

"It just bobbled a little, and then I banged it in the upper 90. I couldn't have asked for anything better. I am very happy about it."

The presence of Snoop Dogg -- who is working at the Olympics for US television -- in the crowd in Paris provided more excitement for many spectators than the game itself.

Japan sat back and allowed the USA to have most of the possession, which they did without showing a cutting edge.

Their front three of Rodman, Mallory Swanson and Sophia Smith were impressive during the group stage but found the going tougher against Japan's back five.

That was until Rodman struck midway through extra time, as she controlled a long diagonal ball by Dunn on the right, turned Hikaru Kitagawa inside out and fired a shot high into the far corner of the net.

It was her third goal in four games at the tournament, making her the USA's joint top scorer alongside Swanson.