The away side took control of the encounter in the opening half and looked the more likely to score when McGugan forced an early save from Lee Grant.
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Burnley managed to cause trouble towards the end of the first 45 minutes from a corner, but Billy Sharp was there to clear the danger.
Dexter Blackstock tried to open the floodgates in the early stages of the second half by launching a shot towards goal, but Grant saved comfortably.
Following a spell of pressure, Burnley managed to take the lead through Junior Stanislas, who adjusted his feet to take a shot towards goal. His effort took a big deflection off Chris Cohen to soar past Karl Darlow.
Sam Vokes tried to double Burnley's lead by taking a right-footed shot from just outside the penalty box, but he was unable to trouble the keeper as it flew wide.
There was eventually some late drama for Forest, who managed to clinch a draw courtesy of a penalty that was slotted in by McGugan.