* West Ham beat Southampton 3-0 at the London Stadium
* Joao Mario fired West Ham ahead with first goal for the club
* Arnautovic doubled the advantage from close range
* The striker volleyed the third on the stroke of halftime
* West Ham dominated the high-tempo relegation dogfight
* Mark Hughes suffered a losing league debut as Saints manager
* West Ham next visit Chelsea, Southampton away to Arsenal (Adds detail, quotes)
March 31 (Reuters) - West Ham United made a big step towards staying in the top flight after two goals by Marko Arnautovic and another by forward Joao Mario gave them a 3-0 home win over Southampton in the Premier League on Saturday.
The result lifted the Hammers to 14th place, on 33 points from 31 games, five more than 18th-placed Southampton, whose manager Mark Hughes suffered a miserable Premier League debut for the Saints, who remain in the bottom three.
Reeling from three successive defeats, the last a 3-0 home loss to Burnley marred by serious crowd trouble, West Ham bounced back with one of their best performances of the season when they needed it most.
“We had a couple of difficult weeks and we wanted to get good results,” Arnautovic told the BBC after an impressive individual display.
“We said that we had to stick together as a team, as a whole club. We knew we could come out of this, we have quality and we showed that today. It was a fantastic performance.”
Mario, loaned to West Ham by Inter Milan in January, fired the home side ahead in the 13th minute with his first goal for the club when he drove the ball into the top corner after a darting run and cut-back by Cheikhu Kouyate.
Arnautovic missed a sitter two minutes later when he broke through and shot wide of the far post with only goalkeeper Alex McCarthy to beat, but soon made amends.
The towering striker tapped in his own rebound in the 17th minute after McCarthy had parried his header following another cross by Kouyate, galvanising a well-behaved home crowd at the London Stadium.
With Southampton on the back foot, Arnautovic sealed West Ham’s win on the stroke of halftime with a clinical volley after a deep Arthur Masuaku cross from the left took out the entire visiting defence.
West Ham left back Aaron Cresswell nearly added insult to injury in stoppage time, shaving the bar with a superb volley from the edge of the penalty area.
The home team’s manager David Moyes was delighted with the outcome, the fans and Arnautovic, previously coached by Hughes at Stoke City.
“They have worked together over the years (Arnautovic and Hughes), Marko is that type,” Moyes said.
“I’m seeing that now, I enjoy working with him and he is showing people why West Ham paid 20 million pounds for him from Stoke.
“The supporters were great and they appreciated the performance of the players. We got the job done early which helped.”
Writing by Zoran Milosavljevic; Editing by Ed Osmond