The victory moved Southampton above Watford up to 10th position with 33 points while their hosts slipped to 13th.
Watford made the perfect start when Troy Deeney scored a fifth Premier League goal in six games inside four minutes, but Southampton led at halftime through goals from Dusan Tadic and Redmond.
Italian forward Stefano Okaka equalised for Watford from close-range with 10 minutes remaining, but Manolo Gabbiadini continued his red hot form after home keeper Heurelho Gomes spilled the ball into his path. Redmond got his second before Abdoulaye Doucoure pulled one back for the hosts.
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(Reporting by Nick Said, editing by Ed Osmond)
