Glovers winger Kevin Dawson bagged the only goal of the game with a fine finish in the 36th minute of the match.
And the Sky Bet Championship newcomers should have secured a more convincing victory at Roots Hall.
Lively midfielder Sam Hoskins had two shots saved by Shrimpers goalkeeper Daniel Bentley in the first half while Joe Edwards volleyed just wide of the left post from long range.
But Dawson made no mistake when teed up by Hoskins, firing an angled 16 yard shot in to the left hand side of the net.
After the break, Yeovil striker Michael Ngoo had a 20-yard shot impressively held by Bentley before he also shot just wide of the right post.
But Southend rarely threatened and registered their only effort of the evening on target in stoppage time when Mark Phillips had a header tipped wide of the left post by Marek Stech.