It made him only the fifth goalkeeper to score in the English top flight since the Premier League was launched in 1992, but Jay Rodriguez's 42nd-minute equaliser prevented Begovic from being the match-winner.
Southampton took a giant stride toward safety with the win, which lifted Mauricio Pochettino's team seven points clear of the relegation zone.
United boss Ferguson could hardly have selected a more attack-minded line-up but once again his defence let him down as the league leaders fell behind after two minutes.