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.
In a bizarre quirk of the fixture, the sides played each other for the second week in a row, with Southend defeating Burton 1-0 on the last day of the regular season.
And it was Phil Brown's men who started brighter, with Will Atkinson and Barry Corr having early chances.
Burton goalkeeper Dean Lyness then made an excellent save to keep out Atkinson in the 29th minute as Southend continued to press.
But after having a good effort saved eight minutes earlier, McGurk did score, showing composure to lift a shot over Bentley to give his side a boost heading into the break.
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.
