The Hammers have adapted to life in the Premier League far better than the side that finished above them in the Championship and picked up their fourth win of the campaign today.
After a dour first half at Upton Park, Sam Allardyce's men came flying out of the blocks after the restart and netted twice in a three-minute spell.
Noble broke the deadlock with a 40-yard free-kick that drifted past debutant goalkeeper Artur Boruc, before captain Kevin Nolan tapped home a Yossi Benayoun cross at the back post.
Southampton threatened a comeback when Adam Lallana exquisitely fired home, but Noble netted a penalty before substitute Modibo Maiga superbly curled home to secure the three points.
West Ham looked the brighter side early on but Southampton earned the game's first corner with Jay Rodriguez inches away from directing home Jason Puncheon's loss cross.
It was one of several threatening moments by the visitors for whom goalkeeper Boruc was looking shaky.
The former Celtic man became the third different goalkeeper to start for Saints this season and had Andy Carroll to thank for not making the most of an awful clearance early on.
Boruc was playing behind a re-jigged backline in east London as Southampton juggled injuries and attempted to thwart West Ham's aerial threat.
Jos Hooiveld returned to the side as a result of the changes and had to be alert to clear a James Tomkins header off the line.
The Dutch defender saw his own header on goal saved by Jussi Jaaskelainen moments earlier and in the 21st minute Rodriguez put a snapshot just wide.
The £6million striker also fired a free-kick over as Saints tried to break the deadlock, with team-mates Maya Yoshida and Guly do Prado soon miscuing their own long-range efforts.
There were fears for Tomkins when he appeared to twist his knee, but he continued after treatment as West Ham upped the ante.
The home side were struggling to create any clear-cut chances, though, as Southampton went into half-time without conceding for the first time since their return to the Premier League.
However, the Saints defence was breached less than a minute into the second half.
Collins could not quite get a toe on Noble's floated 40-yard free-kick, but it bounced in the six-yard box and flew past Boruc.
The opener was followed moments later by West Ham's second after a poor Do Prado pass was not dealt with by Yoshida.
Benayoun won the ball from the Japan international and his low cross was met at the back post by Nolan, who tapped home from close range.
Only the fine reactions of Boruc prevented the Hammers captain making it three in the 61st minute as he ghosted in and directed a quickly-taken free-kick goalwards.
The save proved invaluable as Saints reduced the deficit two minutes later when Lallana turned beautifully to strike a half-volley past Jaaskelainen from close range.
The goal came thanks to the hard work - and wayward shot - of Rodriguez, who was replaced by Rickie Lambert immediately afterwards.
Saints' top scorer was surprisingly left out of the starting line-up and came on at the same time as Emmanuel Mayuka, although it was the former that made an immediate impact.
First the 30-year-old saw a 20-yard free-kick just go over, before heading a Nathaniel Clyne cross wide.
Southampton were threatening to quieten the home support but undid all their good work when Fonte handled as he challenged Carroll.
Noble fired home the resulting spot-kick, allowing the Hammers to coast from the 72nd minute onwards.
Mayuka tested Jaaskelainen as West Ham endured some nervy moments, but Maiga put the match out of sight three minutes from time, running at the Saints defence and sending a curling left-footed effort home.