The victory leaves the young Hatters five points adrift of league leaders Leyton Orient - who take on Watford at the weekend - with Paul Driver’s side still to play two more games this season, at Portsmouth at the weekend and Crawley next Tuesday.
Against the Shrimpers, Luton went ahead on the half-hour mark when Zane Banton finished well with a left-foot shot from 15 yards.
In wet and windy conditions the Hatters doubled their lead as Arel Amu blasted home from inside the penalty area four minutes before half-time.
The Town were well on top, and their dominance was rewarded on the hour mark when Luke Trottman took a lovely pass from Charlie Smith to volley home from 15 yards to make it 3-0.
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Leeroy Magaraushe hit the crossbar in injury time as boss Paul Driver said: “Given the difficult conditions it was an excellent all round performance against a Southend side who are always tough to play.
“The most pleasing aspect of our game was our decision making and it is always good to keep a clean sheet.
“Our defending has been a particular highlight of our season and it’s a testament to the lads at the back that we have the best defensive record in the league, which, for such a young back-line, is fantastic and something we can really build on next season.
“The win keeps up our chances of winning the title but we’re relying on a favour from Watford and we have to win both of remaining two matches.
“Our game against Portsmouth at the weekend is likely to be the match that decides who finishes in second and third place but at the start of the season I would have bitten your hand off for a top three finish.”
Town: Barnes, Jibodu, Hawkes, Rees, Chabata, Jules (Stephens), Trottman, Smith, Amu (Tayali), Banton, Magaraushe.
Subs not used: Carpenter, Kirkpatrick, Amadi.