Southampton equalised three minutes before half-time when James Ward-Prowse's excellent deep cross picked out Jay Rodriguez, whose downward header bounced over Begovic and into the net, but Begovic opened the scoring at the Britannia Stadium with a wind-assisted clearance from deep inside his own penalty area.
But 26-year-old Begovic's massive kick downfield was allowed to bounce by Southampton's defenders and it then looped up over Polish goalkeeper Artur Boruc, who had come too far off his line.
Begovic, who looked slighty embarrassed by his strike, joins Peter Schmeichel, Tim Howard, Brad Friedel and Paul Robinson as a goal-scoring 'keeper in the Premier League.
It was just Stoke's seventh goal in 10 Premier League games this season and, with one goal to his name, Begovic is now the joint leading scorer for Mark Hughes' shot-shy team in the top flight this season.
Begovic admitted he felt sorry for Boruc so didn't want to rub it in by going over the top with celebrations.
"I feel bad for Artur Boruc when that happens,'' he said. ``It does not make a goalkeeper look good and after it I did not want to celebrate against him.
"It's the worst conditions you can play in. The wet you can deal with but the wind makes it difficult. You don't know where the ball is going to go.
"It's a good point for us. Hopefully we can keep the confidence going and I can get a couple more goals!''
Boruc insisted the wind made it impossible to deal with Begovic's kick, but he vowed the embarrassment wouldn't affect him.
"I'm really sorry for my team-mates and our supporters but what can I say? What happens, happens and I need to bounce back. I promise to get those two points back.
"These kinds of things happen to goalkeepers. It has happened before and will happen again.''
Begovic's remarkably quick effort was short of the fastest ever Premier League strike, which was scored in 10 seconds by Tottenham defender Ledley King at Bradford City in December 2000.
Elsewhere, Steve Bruce enjoyed victory over his former club as
Hull City won 1-0 at the KC Stadium against a
Sunderland side which played the second half with nine men.
Hull went ahead on 25 minutes when Liam Rosenior's cross from the right was headed past his own keeper by Sunderland defender Carlos Cuellar at the near post.
A lengthy stoppage ensued after Sunderland keeper Keiren Westwood was injured and he was eventually forced off before the visitors' day got worse following two red cards in added time.
Cattermole was shown his seventh red card in the Premier League following a lunging challenge on Ahmed Elmohamady before Andrea Dossena was dismissed after an awful tackle on another ex-Sunderland player - David Meyler.
Crystal Palace slipped to a ninth defeat in 10 games after goals from Saido Berahino and Gareth McAuley earned West Brom a 2-0 win at The Hawthorns.
West Brom made the breakthrough on the stroke of half-time when Stephane Sessegnon got down the left and rolled the ball across the edge of the area for substitute Berahino to finish past Julian Speroni.
The Baggies made sure of the points seven minutes from time when Chris Brunt drilled over a corner from the left and McAuley powered in to head home.
West Ham are still searching for a first home win since the opening day of the season after being held 0-0 by Aston Villa at Upton Park.
