Byron Harrison's strike in first-half injury time had handed Cheltenham the advantage but Corr's arrival on the hour lifted the visitors.
Within a minute he had seen his header strike team-mate Jamar Loza on the line with Southend skipper John White then having an effort kept out by Scott Brown in the home goal.
The visitors levelled in the 64th minute when Corr pounced on a loose ball and steered his 15-yard shot into the bottom left-hand corner.
Three minutes later and it was 2-1 to the Shrimpers when the impressive Kevan Hurst stabbed the ball past the advancing Cheltenham keeper.
Harrison's goal, a well-struck volley from 20 yards, had come against the run of play after Lee Barnard had looped a header just wide for the visitors while Hurst had forced Brown into a flying save.
The closest the Robins came to levelling was an 84th minute strike from substitute Zack Kotwica which keeper Daniel Bentley just managed to keep out.