The Bees went in front with a well worked goal in the 29th minute when Paul Hayes rolled the ball in to the path of Tom Adeyemi who fired in to the bottom left hand corner of the net from 12 yards.
Brentford then doubled their lead nine minutes later when a low, right-wing cross from Sam Saunders was diverted past his own goalkeeper at the near post by Ryan Cresswell.
But, within a minute, the Shrimpers were back in the game when Sean Clohessy's deep right wing cross picked out Corr at the back post and the Irishman headed home via the underside of the crossbar from six yards.
Corr then levelled the game in the 53rd minute when he was left all alone by Brentford defence trying to play offside and headed Kevan Hurst's right wing free kick in to the net.
Southend then almost won it late on when Gavin Tomlin had a header superbly saved by Bees goalkeeper Simon Moore.
