© PA Photos
In an uneventful first period, James Tomkins had the best opportunity to break the deadlock when Artur Boruc failed to clear his lines with a punch but the Hammers defender was unable to avoid Jos Hooiveld on the line.
Sam Allardyce's half-time words had the desired reaction as the hosts took charge of the game with two goals in quick succession after the break.
Noble opened the scoring with a long-range free kick that evaded everyone on its way into the bottom corner of Southampton's goal.
The visitors were rocked by the goal and fell further behind two minutes later when Boruc parried a Yossi Benayoun effort into the path of Kevin Nolan, with the midfielder making no mistake from close range.
Southampton's comeback was short-lived though, as the hosts were awarded a penalty when Jose Fonte handled the ball inside the area and that decision allowed Noble to double his tally from 12 yards.
The Hammers were able to relax following the third goal and completed the victory when substitute Modibo Maiga curled in from the corner of the box.