The Shrimpers consolidated their place in the play-off places and all but extinguished any hope the Seagulls had of forcing their way into the top six.
The visitors started brightly and Darryl Flahavan had to be alert to thwart Glenn Murray’s effort but their optimism was dealt a heavy blow in the 23rd minute when Mark Gower smashed home the opener.
That goal galvanised the home side and they were soon 2-0 up when Gower fed Adam Barrett who made no mistake by rasping home.
The Seagulls tried their best to get back into the match but Murray and Nicky Forster could not beat Flahavan. But as the second half developed, the home side began to take control once more with Nicky Bailey twice being denied.