Arsenal, third in the Premier League, looked to have overcome the first-half sending-off of Dennis Bergkamp when substitute Robert Pires struck from close range 12 minutes from time.
United kept pushing forward, however, and won a penalty when Arsenal defender Philippe Senderos handled the ball in the area and Andy Gray calmly converted the spot-kick to earn his side a replay.
Arsenal were reduced to 10 men after 35 minutes when Bergkamp, captain for the day in the absence of the rested Patrick Vieira, was controversially sent off for pushing an opponent in the chest during a confrontation between players of both sides.
United's Danny Cullip headed the ball into the net from eight metres just before halftime but the effort was harshly disallowed for pushing.
Arsenal forward Jose Antonio Reyes twice went close with long-range strikes before midfielder Mathieu Flamini's firm shot was pushed away by United goalkeeper Paddy Kenny and Pires forced the ball home from six metres.
Bolton Wanderers play Fulham, Charlton Athletic meet second division Leicester City, Southampton entertain third division Brentford and holders Manchester United travel to Everton later on Saturday.
Premier League leaders Chelsea visit Newcastle United, second division Burnley play Blackburn Rovers and Tottenham Hotspur face Nottingham Forest on Sunday.
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