The Saints striker put his side in front on 16 minutes, firing into the bottom-right corner from 20 yards.
Ings then made the score 2-0 on 70 minutes, intercepting Ben Foster's throw before finishing low past the Watford goalkeeper for his 18th goal of the season, leaving him only one behind Golden Boot leader Jamie Vardy.
Jan Bednarek's own goal with 11 minutes remaining gave Watford hope of a comeback but that was dashed three minutes later when James Ward-Prowse curled in a superb free-kick.
Southampton's eighth away victory of the season moves them to 13th place on 40 points.
A run of four matches without a win leaves Watford 16th on 28 points, one point clear of the bottom three.
The Hornets have played a match more than all but one of the four teams below them.
Watford: 4 Jul v Chelsea (A)
Southampton: 5 Jul v Man City (H)