The defeat took the Robins' league run without a win to seven matches, while the Shrimpers made it five wins from six games.
The Robins blew a great early chance when 10-goal leading scorer Simon Cox released Michael Timlin, but he was offside.
That mistake was punished in the 12th minute when Jean-Francois Christophe passed to Kevin Betsy on the right wing and his cross was headed home by Revell from six yards.
Moments later, Blues skipper Adam Barrett headed over Peter Brezovan's goal from a Lee Sawyer centre.
But Swindon did not let their heads drop and went onto create the better chances.
The best came when Timlin's deflected cross was turned onto the right post by goalkeeper Adam Federici and Barrett cleared off the line.
The visitors then saw Lee Peacock half-volley wide from Jack Smith's cross, before former Southend striker Billy Paynter's shot on the turn was turned over by Federici.
Peacock headed the resulting Timlin corner over but Southend had the last say off the half when Simon Francis' 30-yard effort was held by Brezovan.
The Shrimpers dominated proceedings early in the second half but were wasteful with their chances with James Walker getting the only shot on target and that was blocked by Brezovan's legs.
Swindon got on terms in the 61st minute when Timlin's cross from the left was headed back across goal by Cox at the back post and Paynter headed in from six yards, injuring himself on the process.
The Shrimpers immediately blew a gilt-edged chance to take the lead when Brezovan missed a throw-in, the alert Revell passed to Walker but the striker fired wide of the open goal.
Southend manager Steve Tilson brought on Laurent for the injured Revell on 67 minutes and three minutes later the French striker scored his first goal of the season with a headed goal from 12 yards off Peter Clarke's right-wing cross.
Laurent thought he had bagged a second seven minutes later but it was ruled out for offside.
Substitute Barry Corr should have salvaged a point for Swindon but he dithered in a one-on-one with Federici and the Southend keeper palmed the ball away.