The midfielder flicked home a neat header to earn a 1-1 draw after Jason Scotland had initially put the Welsh side ahead.
It saw Forest continue their recent resurgence in which they have taken seven points from a possible nine in three games against promotion-chasing sides.
Forest should have taken the lead in the first minute as Paul Anderson picked out Robert Earnshaw on the edge of the six-yard box only for the striker to fire wildly over.
Anderson came rather closer to scoring against his former club as he cut in from the right and flashed a fearsome shot across the face of goal.
Joe Allen also came close for Swansea with a carbon copy effort that had Paul Smith scrambling across his goal to cover as it fizzed narrowly wide.
It took a superb, sliding challenge from Kelvin Wilson to deny Scotland a certain goal as he looked to connect with a Jordi Gomez cross at close range.
Forest were getting closer to a goal themselves, however, with Isaiah Osbourne powering a rising shot against the bar after a clever exchange with Guy Moussi.
Dorus de Vries then had to swat away a crisply struck free-kick bent around the wall by Chris Cohen.
Loan signing Gary McSheffrey should have had a debut goal for Forest after Joel Lynch had delivered an enticing cross to the far post, but the forward side-footed wide as the half came to an end with both sides wondering how they hadn't scored.
It was Forest who look the most likely to break the deadlock after the break with de Vries making a spectacular, acrobatic stop to palm away a Cohen drive that was bound for the top corner.
And Earnshaw was also denied by the keeper after robbing Alberto Serran of possession, although McSheffrey would have been certain to score had the striker squared the ball to him instead of shooting.
It was a flowing, incisive move from Swansea that brought the game's first goal, however, as the Welsh side edged their way into the lead in impressive style.
Jordi Gomez showed a great piece of skill to control a lofted pass over the Forest back-line before flicking a clever ball to Scotland, who was left with the simple task of slotting the ball into an exposed goal from close range.
McGugan, who had been left out of the Forest starting line-up as Billy Davies opted to rest him following a demanding run of fixtures, came off the bench to fire the home side back into the match.
McGugan had been on the pitch less than ten minutes when Lynch delivered a perfectly flighted cross towards the near post which the midfielder converted with a precise header inside the post.
Smith had to stretch himself full length in the dying stages to smartly palm a Gomez drive around the post.
Earnshaw twice came close to snatching it for Forest, seeing a flicked effort blocked after latching onto McGugan's lofted pass over the top and then firing a acrobatic kick over the bar.