In their first game since fans charged onto the pitch during their 3-0 defeat to Burnley, the Hammers surged to a comfortable lead at half-time with a double from Arnautovic (17, 45+4) and a powerful strike from Joao Mario (13).
Hughes, who was taking charge of his first Premier League game for Southampton, has history with Arnautovic after he publicly criticised him following West Hams game with Stoke earlier this season. The West Ham striker celebrated his opener by angrily shouting towards the away dugout, presumably with Hughes his target.
The result sends West Ham five points clear of the drop zone while Southampton remain in the bottom three, two points from safety with Arsenal (a) and Chelsea (h) their next two games.
West Ham skipper Mark Noble called for the home fans to stick with their team for this crucial encounter, which subsequently turned out to be an easy request as the Hammers started full of energy.
On 13 minutes, a quick counter-attack down the right flank - triggered by Cheickhou Kouyate - resulted in Mario firing home a spectacular strike from 18 yards out.
The home fans sensed nervousness in the visitors and roared their team on. Arnautovic fired a gilt-edged chance wide on 15 minutes but made amends 90 seconds later when hammering home a rebound after his initial header from close range was palmed back to him.
Southamptons front pair of Charlie Austin and Manolo Gabbiadini were mere bystanders as the Hammers controlled the game in every department. The third goal came during first-half injury-time when Arnautovic volleyed home a pin-point Arthur Masuaku cross.
The introduction of Shane Long improved Hughes men after the break but they never looked capable of giving Joe Hart anything serious to think about.
Arnautovic hunted his first Premier League hat-trick but couldnt add to his tally despite testing McCarthy with some long-range efforts - his eighth and ninth goals in his last 13 games were more than enough for the comfortable Hammers.
