Nigel Reo-Coker drove forward to have a shot parried for a corner during the opening exchanges before he played a major part in the opening goal of the game.
Picking the ball up from Luke Chadwick in his own half, he ran to the edge of the box to play it to Marlon Harewood who made no mistake in despatching the ball into the far bottom corner for his first goal of the season.
Broughton nearly equalised when Gower's cross was met at the far post with a glancing header, but it whistled just wide.
Marlon Harewood came close to adding to his tally when he hit a crisp shot on the turn only to see Bart Griemink parry it onto the post where it then span away for a corner.
The second half started quietly, and Southend came closest to scoring when a Kevin Maher strike from 25 yards went just wide of a diving James Walker.
Mark Noble became the third debutant on the night when he came on for Luke Chadwick midway through the second half and shortly afterwards Teddy Sheringham replaced Sergei Rebrov.
West Ham survived another scare when a scramble led to Chris Cohen requiring treatment - and gave the visitors a corner.
But Sheringham's presence lifted the Hammers, with Nowland and Reo-Coker testing Griemink, while at the other end Maher forced a save from Walker with a header.
And, despite Southend's threats, Marlon Harewood broke down the middle in the 90th minute to tuck the ball under Griemink.
Adam Nowland and Tomas Repka were booked for West Ham; Broughton and Maher for Southend.
James Walker and Elliot Ward made their full debuts, while Trent McClenahan, who came on for his debut on Saturday at Crewe, made his first start for the club.
Darren Blewitt and Moses Ashikodi had never previously been on the bench, while Rufus Brevett overcame a slight injury to play - and be named captain.
Additions to West Ham's injury list from Crewe were Hayden Mullins, Matthew Etherington, and Anton Ferdinand.
TEAM: Walker, Repka, Brevett, Harewood, Cohen, Rebrov [Sheringham], Nowland, Reo-Coker, Ward, McClenahan, Chadwick [Noble].
Subs unused: Bywater, Blewitt, Ashikodi.