The result on the night was enough to give Steve Davis's side a 3-2 aggregate victory.
The visitors were ahead at the break when AJ Leitch-Smith cut inside the penalty area before he fired into the far corner.
They could have doubled their lead soon after, but Byron Moore inexplicably fired over the bar after he had been gifted an opportunity by goalkeeper Cameron Belford.
Southend were dominant after the break as they looked for a goal to get them back in the game and they nearly had it when Michael Timlin and Freddy Eastwood both hit the woodwork.
The home side finally found a lifeline just after the hour as Neil Harris poked home after some poor defending from Crewe.
However, Crewe extended their lead with six minutes to play when Max Clayton's finish snuck past Belford.
There was still time for late drama as Ryan Hall nodded in to give his side hope, but the visitors were able to hold out for the aggregate triumph.