The vocal jousting between the fans had barely started when the striker opened his account with his 19th goal of the season after 38 seconds.
The ball dropped to Shrimpers centre-back Efe Sodje and his back-pass was intercepted by the 31-year-old, who lashed the ball into the bottom right of Darryl Flahavan's goal.
Southend struggled to penetrate the U's defence, although goalkeeper Dean Gerkin did well to turn a Freddy Eastwood shot out for a corner.
The rest of the first half was not much to write home about, but things improved after the break as Alan McCormack and Peter Clarke tested Gerkin.
But Cureton put the visitors in the driving seat on 63 minutes when he latched on to strike partner Chris Iwelumo's pass and composed himself before rifling a 25-yard shot past Flahavan.
Gerken then denied McCormack and Eastwood before the latter headed just over the bar, with former Shrimpers youngster Gerken beaten.
However, Colchester ensured a second 3-0 league win over their Essex neighbours this season when Cureton struck for the third time on 79 minutes.
He latched on to Chris Barker's pass from the left before lobbing the advancing Flahavan from 12 yards.
The win lifted Colchester up to ninth ahead of their match with Southend's relegation rivals Leeds United on Monday.
The Shrimpers remain third from bottom and face a Preston side hunting promotion on Monday.