McGurk scored the only goal of Sunday's first leg at the Pirelli Stadium, dinking over Southend goalkeeper Daniel Bentley after linking well with team-mate Billy Kee.
His goal, scored on the stroke of half-time, saw Gary Rowett's side head home happier, despite the red card given to defender Ian Sharps on the hour mark.
Southend, though, will take some encouragement from their performance ahead of Saturday's second leg.
And it was Phil Brown's men who started brighter, with Will Atkinson and Barry Corr having early chances.
Sharps – initially booked in the 57th minute for handball – was then sent off three minutes later for tripping Atkinson.
Southend's numerical advantage helped them apply some late pressure, but John Egan's late strike was superbly saved by Lyness, while they also had a penalty appeal turned down, as the hosts hung on for a first-leg win.
