By Mike Collett

LONDON (Reuters) - Mexico reached the men's Olympic soccer final for the first time when they came from behind to beat Japan 3-1 in front of more than 82,000 fans at a rainy Wembley Stadium on Tuesday.

Japan went ahead with an arrowed shot from Yuki Otsu from outside the area after 12 minutes but their hopes of emulating the women's team, who reached their final by beating France at Wembley on Monday, faded as Mexico gradually took control.

The equalizer came in the 31st minute when Marco Fabian nodded in a flicked on corner from Giovani Dos Santos from close range and Mexico, who were the better team, deservedly went ahead with a sizzling shot from Oribe Peralta after 65 minutes.

Substitute Javier Cortes completed the scoring with an angled shot after a solo run in the third minute of added time.

Mexico will meet the winners of Tuesday's other semi-final between Brazil and South Korea at Old Trafford (2.45 p.m. EDT) in Saturday's showpiece at Wembley while Japan will play the loser of that game for the bronze medal at Cardiff on Friday.

(Reporting by Mike Collett; editing by Ken Ferris)