Southend dominated the opening spell, but it was Robins winger Andy Lindegaard who had the first shot on goal when he fired a tame 20-yard effort straight at Steve Collis.
That sparked the Robins to life but they went a goal down on 11 minutes when Mark Gower's cross from the left was headed home from 12 yards by Lee Bradbury.
Cheltenham replied with a 30-yard Paul Connor shot that failed to trouble Collis, who then did well to smother a Craig Reid cross while under pressure from John Finnigan.
Gower then saw his shot deflected out for a corner by Andy Gallinagh and the resulting Gower flag-kick was headed narrowly wide by Adam Barrett.
Robin's winger Sosthene Yao unleashed a right-foot shot into the side netting before goalscorer Bradbury shot inches wide in first half stoppage time.
Franck Moussa then denied Dave Bird an equaliser after 55 minutes when he cleared the central midfielder's far post header off the line after another Lindegaard corner from the right was only partially cleared.
Reid then saw his looping shot safely gathered by Collis after Bird's ball into the box was headed clear to the striker.
Cheltenham continued to carve out the better chances, with skipper Finnigan's 30-yard effort going narrowly over the bar with Collis beaten.
Southend finally created a chance when Belgian midfielder Moussa was inches wide from the edge of the box following Barrett's lay-off.
But Cheltenham were rewarded for their enterprise when Finnigan got them on level terms in the 70th minute.
A long clearance released the captain upfield and he swapped passes with Yao before firing home from six yards.
Deep into injury time Peter Clarke brought down Shane Duff from Lindegaard's corner and referee Keith Hill pointed to the penalty spot.
But Finnigan blew a chance to secure the win for his side when Collis dived to his right to save the spot-kick.
The game went into extra time and the Shrimpers took the lead when Bradbury crossed the ball to Barrett and the centre half's left foot shot went in off the underside of the bar on 102 minutes.
And Bradbury got his second of the night from the penalty spot after Barrett was fouled in the box while attacking a Black corner.
The striker fired straight down the middle with Higgs diving to his left.
Bradbury then completed his hat-trick on 117 minutes after racing onto a loose ball and slaming home an unstoppable shot from 14 yards to seal a victory that was much closer than the final scoreline suggested