The original first-round fixture at Deepdale finished goalless and it was the same story after the first half of Tuesday’s replay, which was a pretty even affair.
Southend had the better chances, with Preston goalkeeper Thorsten Stuckmann keeping out a powerful Dickinson free kick and turning a Neil Harris header wide.
Preston upped their game as the half wore on and saw Danny Mayor shoot wide after a run from the halfway line before goalkeeper Luke Daniels went close to punching a Paul Parry free kick into his own net.
But Southend took the lead 10 minutes into the second half when Ryan Hall’s shot was parried by Stuckmann to Bilel Mohsni, who headed the ball for Dickinson to unleash a right-footed volley into the net.
Paul Coutts had an effort ruled out for offside on 65 minutes and, despite applying a lot of pressure, the visitors were unable to equalise against the League Two leaders.