Watford striker Troy Deeney scored a quick-fire double early in the second half at Hillsborough to take his tally to 20 for the season after first-half goals from Gabriele Angella and Lewis McGugan put the Hornets on course for a first away win in 15 games.
Wednesday's on-loan striker Benik Afobe pulled one back for the home side but they were well beaten.
Watford manager Sannino refused to rule his team out of play-off contention after the Hornets' first win on the road since October 5.
The result, a repeat scoreline of Watford's win at Hillsborough last season, leaves the Hornets eight points off the top six, with a game in hand.
"I always said before that we don't have to have any regrets when the season finished," he said.
"This division is a very tough division and every game I'm catching something and trying to understand more and to be prepared for next season.
"I have seen very good teams in this division with very good managers and it's not like the old English football with the ball always in the box. In this league you can see teams that try to move the ball and play good football."
He added: "It's a long time since Watford have won away; too many losses and too many draws. I'm very happy for our fans and our players.
"The confidence grew during the game because we were able to pass the ball and move the ball better than in the past.
"I'm pleased that we scored four goals because our little problem is the last minutes of games - because we always concede goals. Every match when I have been in charge, the last 10 minutes have cost us a lot in terms of points."
Wednesday boss Stuart Gray missed the heavy defeat to attend the wedding of his son, an agreement which was put in place when he joined the club as a coach under former Owls boss Dave Jones in December 2012.
Coach John Deehan played down the absence of head coach Gray after his side were thrashed 4-1 by Watford in the Sky Bet Championship.
"I haven't spoken to Stuart at all today, everything was done yesterday," said Wednesday coach John Deehan, who was put in joint charge of the team along with fellow coach Lee Bullen.
"I think you know the circumstances he's in and with all due respect, family comes before football.
"I think the players are professional enough to just get on with it. We've just had a chat in the dressing room between all of us and we've had some very strong opinions.
"Football players don't like getting beaten in games and they don't like getting beaten in the manner they did today.
"The performance fell below the level we've been performing at before.
"Their first attack exposed us straight away to pace and to concede that early in the game (the fifth minute) put us on the back foot.
"They've probably got, in Troy Deeney, one of the strongest, most powerful strikers in the league so having to then try and press on, getting the equaliser as quickly as possible, put us in a vulnerable situation.
"It wasn't to be today; today was the day it went against us. We changed shape at half-time to try and become a more attacking-minded team.
"We went out with the best intention of trying to score the next goal, which would've given us an opportunity to possibly even win the game.
"But as soon as it went three and four so quickly it put us on the back foot.
"We've just got to take our medicine and say this is one of the games that went against us."