Long's strike beats Ledley King's effort for Tottenham against Bradford in 2000, when he netted after 9.82 seconds.
Opta had the goal at six seconds.
The Republic of Ireland striker put the Saints ahead right from kickoff at Vicarage Road, blocking Watford defender Craig Cathcart's attempted clearance before cooly lifting the ball over Hornets goalkeeper Ben Foster.
The goal was Long's fourth of the season, and came in his 23rd Premier League match in 2018-19.
Christian Eriksen scored after 10.54 seconds for Tottenham against Manchester United last season.
Southampton are five points clear of the relegation zone, and with a game in hand over 18-placed Cardiff City and Hasenhuttl knows what his side still need to do.
Long then blocks Cathcart's lofted pass, and fortuitously deflects the ball goal-bound.
Redmond was also denied by a good save from Foster and Long headed two other presentable chances off target.
Southampton could not hang on and Gray swept home from close range to lift Watford up to seventh and keep Hasenhuttl's men looking over their shoulders a little longer.
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