The Irish striker had gone 12 games without a goal for the Shrimpers but he rediscovered his scoring touch to help fire Phil Brown's side to a third successive league win.
Corr's first goal came in the 21st minute when Kevan Hurst's brilliant right-wing cross picked him out at the far post to bundle the ball home.
Fleetwood had been on top up until the Shrimpers' goal with striker David Bell having two low shots saved by Daniel Bentley.
The Southend goalkeeper then also did well to parry out a well-struck shot from Antoni Sarcevic.
But the Shrimpers made sure of their win in the 81st minute, with Corr on target from the penalty spot.
The spot-kick was given after Will Atkinson was brought down by Liam Hogan and Corr slammed his 12-yard shot high in to the left hand side of the net.