Swindon, with nine first-team players out injured and a further three suspended, shocked Southend by taking a second-minute lead.
Blues goalkeeper Steve Collis could only parry Andy Nicholas' shot from the left and Simon Cox reacted quickest to race in and slam the loose ball home from six yards.
The Robins continued to look stronger as the Shrimpers struggled to get their passing game together.
Leon Clarke went close to equalising but his volley crashed against the crossbar, before his side got back on terms on 32 minutes.
Steve Hammell's free-kick into the box found Adam Barrett 12 yards out and he headed his sixth goal of the season past a static Town defence.
Both sides struggled to get a grip on the game in the second half as the combination of strong winds and pouring rain took their effect.
Swindon appealed for a penalty for handball after skipper Hasney Aljofree's shot went into a melee of players.
And Aljofree's last-ditch tackle denied Leon Clarke a shot from close range following good work down the left by Nicky Bailey.
Nicholas went close with a header after Blues defender Peter Clarke headed Chris Allen's corner from the right clear.
But Michael Pook went closest for the visitors when his rising 30-yard shot went inches over Collis' crossbar.
Yet in the last minute of the three minutes referee Stuart Atwell added on, Leon Clarke squared the ball for Gower to curl a sweet 16-yard shot past Petr Brezovan.