Corr fired home the only goal of the game in the 38th minute to secure a third successive win for the fifth placed Shrimpers and record his ninth in 11 games.
The game also saw Southend goalkeeper Daniel Bentley equal a club record by keeping a 10th clean sheet in a row at home and he was called into action several times in the first half.
The 21-year-old was forced into making an early save when he denied Kayode Odejayi from close range before he also tipped a low, 20 yard shot from Danny Holmes around the right post.
However, the Shrimpers hit back and bagged the only goal of the game just before the break when Will Atkinson’s right wing corner picked out Corr who neatly fired home at the near post.
Southend were initially on top after the break, with Atkinson and Adam Barrrett both going close before second from bottom Tranmere enjoyed plenty of possession late on.
But they were unable to find a way past a resolute Shrimpers defence and remain entrenched in the relegation battle.