The home side's play-off hopes already needed a miraculous resurrection over the last six games of the season, but they looked set for a first home win since January and a return to the top half after Junior Stanislas' second-half strike.
Forest played some attractive football and remain in the top six, but looked every inch a team playing their second match in three days and rarely threatened to add to their six wins and a draw since Billy Davies' return as manager - until McGugan's late strike.
After just four minutes Gonzalo Jara played Lewis McGugan in down the right and his cross picked out Billy Sharp, whose header from six yards was well tipped over by Lee Grant in the Burnley goal.
At the other end Charlie Austin cut-back for Chris McCann but the veteran midfielder scuffed his effort.
With 12 minutes gone Ross Wallace delivered a delicious through ball with the outside of his left foot to play in Austin, but the former Swindon striker blazed harmlessly over from the edge of the box.
Forest were playing the better football, and midway through the first half McGugan's superb turn in midfield ignited a visiting attack which ended with Grant producing a good save to keep out Henri Lansbury's curling 20-yard effort.
The home side might have had a penalty when Chilean full-back Jara clumsily bundled into Austin as he looked to get on the end of a Kieran Trippier cross, while moments later Stanislas broke free down the left only to see his shot well saved by Karl Darlow.
The second half suddenly came to life after 68 minutes when Stanislas gave the home side the lead. Having controlled McGugan's corner in his own box, he swiftly broke and found substitute Joseph Mills on the left, before the full-back's cross fell to the former West Ham winger at the back post. His shot deflected off Chris Cohen past a helpless Darlow.
It could have been two a minute later when Austin cleverly played in Vokes, but Darlow came out well to smother the ball at the former Bournemouth striker's feet.
Late on, Grant smartly tipped Greg Halford's late header over the bar and Burnley were comfortably hanging on despite a late handball appeal against Mills in his own box. That was until McGugan slotted home from 12 yards after Kevin Long collided with Lansbury.