Corr scored his first goals since the opening day of the season to maintain Phil Brown's side's good form and prevent their opponents climbing to the top of the table.
Following a quiet start to the contest, Kevan Hurst created some space to cross from the right for Corr to head in a 22nd-minute opener.
Antoni Sarcevic twice came close to grabbing Fleetwood an equaliser before the interval, firstly striking the post from a free kick, before forcing Shrimpers stopper Daniel Bentley into a smart save following a swift counter attack from the visitors, who were one point behind league leaders Chesterfield prior to kickoff.
The second period began similarly to how the first did, and there few signs of anybody adding to the scores until Corr again combined with Hurst to threaten with a 68th-minute header.
The usual suspects were again involved shortly afterwards as Bentley got down to deny the lively Sarcevic with his legs, and that proved to be Fleetwood's final opportunity to equalise.