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|80/1||Stoke are 80/1 with BetVictor to win the FA Cup this season|
And it was also the longest-range goal scored in the league's 21-year history.
In windy conditions at the Britannia Stadium, a clearance from the Bosnia international bounced high over opposite number Artur Boruc to give Stoke a sensational early lead.
The goal is the fourth-fastest in Premier League history, behind behind Ledley King, who scored against Bradford City in 9.9 secsonds, Alan Shearer, who scored against Manchester City after 10.4 seconds and Mark Viduka, who netted against Charlton in 11.1 seconds.
Begovic becomes the fifth goalkeeper to score a Premier League goal, following in the footsteps of Peter Schmeichel, Brad Friedel, Paul Robinson and Tim Howard. The latter's strike also came courtesy of a long punt upfield.
Stoke's surprising opener represented only the fourth goal Southampton have conceded in the league this season.
Begovic previously represented the south-coast club's rivals Portsmouth before joining Stoke in 2010.