Manchester United and Brighton played to a 2-2 tie yesterday in an overtime English F.A. Soccer Cup final before 100,000 at Wembley Stadium.

The teams, which could not break the tie in 30 minutes of overtime, will replay the game at Wembley on Thursday night. The final swayed back and forth on slippery, rain-sodden turf.

Heavy underdog Brighton, relegated to the Second Division of the English League after a bad season, took the early lead on Gordon Smith's goal in the 14th minute and led, 1-0, at halftime. Manchester surged back in the second half to lead with goals by Frank Stapleton after 55 minutes and Ray Wilkins after 72.

Gary Stevens tied the game for Brighton three minutes from the end of regulation time.

The overtime was scoreless with Brighton mounting the biggest threat seconds from the end. But Manchester goaltender Gary Bailey stopped Smith's point-blank shot after he was fed by Mick Robinson on a two-on-one break . . .

President Reagan has signed a congressional resolution offering government support for the efforts of the U.S. Soccer Federation to bring the World Cup Championship matches to the United States in 1986. But the international soccer federation executive committee has already awarded the matches to Mexico.