Adrian was sent off on the hour mark after Sadio Mane got the better of him and he handled the ball outside the area.
But though it looked like the home side – who had 20 shots on target – would get the winner goal their possession deserved, two late saves from substitute Jussi Jaaskelainen ensured the Saints had to settle for their first goalless draw since August.
Sam Allardyce will be happy with the point but concerned as Andy Carroll, having only returned from injury at the weekend, limped through the last 10 minutes of the game.
Southampton – who slip a place to fourth – started the game like a side keen to cement themselves in the Champions League places and West Ham spent the first 20 minutes under pressure.
It was Saints midfielder Victor Wanyama who had the first chance, from 25 yards out, but he swung at the ball and it flew yards over the bar.
Mane followed that up in the 15th minute when he collected Steven Davis’ cross from the right and ran into the box. He managed to knock it past Adrian at his near post but Carl Jenkinson was there to clear it. It was the start of a very bad evening for the Spanish goalkeeper.
Mane had another chance just moments later and this time Carlton Cole saved his teammate after Adrian completely missed the ball when he came out to clear.
Eljero Elia was the next forward to have a go as he beat the offside trap, but Jenkinson was alert to the danger and after being closed down, the Dutch international sent his shot wide.
Allardyce made the first changes; bringing on Matt Jarvis for Enner Valencia after the break – even though the summer signing had mustered the Hammers’ only shot on target.
The visitors altered their shape and though it looked like the plan was to send longer balls in for Carroll – on for Diafra Sakho – the striker spent more time clearing the ball out of his own area.
West Ham’s chances came on the break, as Adrian’s long free-kick found Stewart Downing but he could only send his shot over.
Adrian’s rush of blood came on the hour when Mane, who had been lively all game, nicked the ball from his grasp.
The pair battled for it, only for Adrian to panic and flick the ball away with his hand outside the area, leading referee
Pawson to dish out a straight red card.
Jaaskelainen came on in place of Cole and exuded experience as he twice saved from Graziano Pelle, before thwarting Jose Fonte at his right hand post.
The result sees Southampton drop a point below Manchester United – but remain ahead of Arsenal on goal difference – while the Hammers stay eighth and have 38 points on the board after 25 games.
Southampton: Forster (6), Clyne (6), Fonte (7), Gardos (6), Yoshida (7), Reed (6), Wanyama (7), Steven Davis (7), Mane (7), Pelle (6), Elia (6).
Used subs: Tadic (6), Djuricic (6), Ward-Prowse (6),
West Ham: Adrian (4), Jenkinson (7), Kouyate (8), Tomkins (7), Cresswell (7), Song (6), Amalfitano (6), Downing (6), Valencia (6), Sakho (6), Cole (7).
Used subs: Jarvis (6), Carroll (7), Jaaskelainen (7)
Man of the Match: Cheikhou Kouyate
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