The young striker scored his third goal in two games to give Jim Bentley's side their third win in four matches. Redshaw was in the right place at the right time to drill home the loose ball from eight yards out after Andy Wright's right-wing cross had been headed back across goal by substitute Richard Brodie.
Morecambe were left to hang on in the final minutes of Saturday's League Two encounter after Brodie was sent off for kicking out at Sean Clohessy and Kevan Hurst almost gave the visitors a share of the points with an effort deep into injury time.
The first half saw few clear chances with both defences very much on top. Kevin Ellison produced the first moment of note when he cut inside to swing a left-foot shot wide of the right-hand post before Redshaw drilled an effort narrowly wide from 25 yards.
Southend hit back with Ryan Cresswell heading a Hurst cross just over from six yards and Britt Assombalonga dragged an effort wide after cutting inside from the left.
As the half came to a close Morecambe enjoyed a period on top with Anthony Straker making a vital block from Gary McDonald's shot and Hurst doing well to foil Ellison in the box as he threatened to fire in on goal.