EFL Cup finalists Southampton, beaten by Manchester United last Sunday, were trailing after four minutes as Troy Deeney volleyed in for his 100th league goal for Watford.
Dusan Tadic equalised and Redmond gave the visitors a deserved half-time lead, only for Stefano Okaka to level 11 minutes from time.
Gabbiadini pounced to punish Heurelho Gomes' error and Redmond struck a fine fourth to give the visitors a win that their pace and movement warranted.
There was a nervy conclusion, though, as Watford substitute Abdoulaye Doucoure netted in stoppage time.
Saints' previous Premier League game was the 4-0 win at Sunderland on February 11 and their next is at Tottenham on March 19, so Claude Puel was keen for a victory and got it as his side climbed to 10th place.
It was a Zlatan Ibrahimovic goal three minutes from time which defeated Saints at Wembley.
And little more than three minutes into their only Premier League game in 36 days two Younes Kaboul long throw-ins caused chaos.
From the second, Okaka controlled the ball with his back to goal and laid it off for Deeney to leap and execute a side-footed finish across goal.
It was the Watford skipper's ninth goal of the season and brought up a century of league goals for the club.
Saints responded. James Ward-Prowse and Gabbiadini were denied by Gomes as the visitors stretched Watford's newly-deployed back three.
Next Tadic ran at them and lost the ball, but Kaboul and Miguel Britos got in a muddle as they attempted to clear. The ball broke for Tadic, who fired low across goal into the bottom corner.
Redmond started the move which finished with his first Premier League goal since October.
He ran down the middle, fed Ward-Prowse who played it for Tadic on the right. Tadic pulled the ball back and Redmond finished well across goal.
Watford were also troubled at set-pieces. Gomes tipped over a Tadic volley after Watford cleared a corner only to the edge of the area.
And Gomes saved well to deny Maya Yoshida as the defender stretched to attempt to turn in a Tadic free-kick from wide on the left.
Fraser Forster saved with his feet to deny Okaka and Deeney fired wide soon afterwards.
And Watford levelled when substitute Isaac Success ran at Cedric Soares and crossed to the near post where Okaka tucked in.
Parity was short lived. Saints substitute Sofiane Boufal's shot from 25 yards bounced in front of Gomes, who did not claim it and Gabbiadini reacted first to score.
Saints had a two-goal cushion moments later.
Redmond cut in from the left and ran at a back-pedalling Prodl. The winger unleashed a vicious shot which beat Gomes.
Boufal shot narrowly wide after putting the ball through Kaboul's legs before Doucoure tapped in from a yard out, but time ran out for Watford as Saints celebrated.