The defender headed a Simon Francis free-kick into the top left-hand corner of the net from eight yards in the 54th minute.
And midfielder Christophe blasted home a 20-yard shot into the opposite corner in the 89th minute after being teed up by Franck Moussa.
The Robins were relegated last weekend but had battled all the way to avoid the drop.
And they continued in that frame of mind against Southend with a fast pace that was nearly rewarded as early as the ninth minute.
Left-back Yuri Berchiche crossed from the left byline and found Michael Antonio six yards out from the middle of Steve Mildenhall's goal.
A goal looked certain but instead the striker somehow hooked the ball over the bar.
Southend gradually worked their way into the game and stepped up the pressure, although there was little to really worry Will Puddy, who looked comfortable between the sticks in his first game for the Robins' first team.
On-loan Watford striker Theo Robinson provided the Blues' biggest threat and had the ball in the back of the net from Moussa's corner, only for the effort to be ruled out for offside.
Puddy smothered a low 16-yard Robinson effort before easily holding a cross-cum-shot from the forward.
Robinson then fired a 12-yard effort straight at Puddy, Alan McCormack slammed a driven 30-yard shot wide and Anthony Grant finished the half by shooting wide.
The second half started with Moussa firing into the side-netting before Southend took the lead in the 54th minute.
Simon Francis' free-kick found Barrett eight yards out and the defender headed into the top left corner.
Cheltenham nearly found a quick equaliser, but Mildenhall dived to save David Hutton's free-kick.
The Shrimpers came within a whisker of doubling their advantage when Lee Barnard picked up a poor Puddy clearance and tried an audacious 40-yard shot which went just wide.
Puddy then blocked a McCormack effort before Blues netted their second goal through Christophe.