The Seagulls had the first chance after five minutes when Glenn Murray's right-footed shot was caught by goalkeeper Darryl Flahavan.
Alan McCormack shot wide for the hosts before Brighton striker Nicky Forster did the same thing.
But in the 24th minute winger Gower put the Shrimpers in front after he latched into Simon Francis' upfield pass from his own half and rifled home a left-footed shot from just outside the penalty area.
Southend pressed for a second and saw Lee Barnard's effort parried by Michel Kuipers, before skipper Adam Barrett put the hosts 2-0 up after 30 minutes.
This time Gower was the provider, his pass from the flank finding Barrett on the left-hand side of the box before he fired home from 18 yards.
Tommy Elphick blasted over the bar in reply for Brighton before Nick Bailey failed to put Blues further ahead before half-time when he shot wide from a Gower corner.
Brighton started the second half desperate to find a route back into the game but were thwarted by Flahavan, who saved two penalties in Southend's 3-1 win at Crewe on Saturday.
With 49 minutes gone he caught Murray's shot from 12 yards and then punched clear Forster's effort from the same distance moments later.
Striker Murray then headed over the bar from a Dean Cox corner before Kuipers came to the visitors' rescue when he blocked a left-footed Bailey effort from 18 yards with his feet.
And it was the hosts who had the final say with McCormack firing over and substitute Anthony Grant and Charlie Mulgrew heading narrowly over the top.
Thurrock Blue's Review and Marks Out of Ten
