The striker, who recovered from a hip injury to feature, curled home a fine set-piece with just 13 minutes remaining at the Pirelli Stadium.
QPR’s Junior Hoilett hit the bar before the break but the Londoners did not look like winning for the first time this season as the game wore on.
Instead they became the latest top-flight side to pay the penalty for making multiple changes in the competition, manager Harry Redknapp making nine alterations following last weekend’s 4-0 hammering by Tottenham.
Adel Taarabt, 16 months after his last appearance for the club, and former England winger Shaun Wright-Phillips were among those to come in.
Rio Ferdinand, Steven Caulker, Joey Barton and Loic Remy were among the high-profile names given a night off while goalkeeper Robert Green sat on the bench.
The side fielded found that Burton – unbeaten this season – were certainly not intimidated by their top-flight status.
McGurk tested Rangers goalkeeper Brian Murphy with a snap-shot in the opening minutes and Alex MacDonald twice drove across goal.
Dominic Knowles might also have done better than to pick out Murphy after a neat nod-down by McGurk.
Yet while there was no doubting the home side’s’ enthusiasm and energy, Rangers’ extra quality was occasionally evident.
Burton’s defence was wrong-footed after a Karl Henry drive was blocked but Taarabt shot wide from the rebound.
Taarabt and Wright-Phillips also combined well to tee up a fierce Hoilett drive that cannoned back off the bar.
Hoilett also showed some nice touches to create an opportunity inside the box only to miscue his shot over.
Burton went close again before the interval as the speedy Marcus Harness had a long-range effort deflected wide.
Taarabt shot wide early in the second half but the home side’s spirit showed no sign of dipping and QPR had to scramble clear after a menacing MacDonald free-kick.
Knowles appealed for a penalty after being knocked over by Nedum Onuoha but referee Paul Tierney saw nothing untoward.
Rangers, with Leroy Fer replacing the injured Alejandro Faurlin, struggled to generate any momentum and Wright-Phillips floundered in his repeated attempts to better his 6ft 5in marker George Taft.
Burton got the goal their industry deserved after Harness was crudely halted by Richard Dunne just outside the area. McGurk stepped up and clipped a fine curling shot over the wall and past Murphy.
QPR responded by sending on Bobby Zamora for the ineffectual Wright-Phillips but still it was Burton who forced the pace.
Rangers did summon up some spirit for a frantic finish, which included four minutes of injury time, but Burton stood firm.