Town's Lee Martin had already been denied what he construed to be a penalty, with referee David Webb deeming the contact outside the box, when he reacted angrily to a Henri Lansbury challenge by appearing to hit out at the Forest midfielder to warrant a first-half dismissal.
The visitors were proving a tough nut to crack but their task become gargantuan when Richard Stearman picked up a second yellow card with just over 20 minutes to go after he was harshly adjudged to have caught Andy Reid in the face.
Town dug deep, with Stephen Henderson saving superbly from Reid, but McGugan was to beat the visiting goalkeeper six minutes from time with an effort which took a huge deflection as Forest made it 13 points from 15 since boss Billy Davies' return.
The hosts' pre-match anthem talks of 'mist rolling in from the Trent' and that was all-too prevalent at kick-off. However, the poor visibility did not stop Webb noticing Elliott Ward's scything challenge on Michael Chopra which earned the Forest centre-back an early caution.
Neither goalkeeper had been troubled until Martin drove just over Karl Darlow's crossbar from distance. While, at the other end, Henderson was in the right spot for Cox's deflected effort.
Henderson made an even better stop moments later to deny Lansbury, who danced around a couple of defenders before drilling against the stopper's left arm.
Ipswich were then left perplexed when Martin was tripped around the edge of the area by a combination of two Forest players with Webb awarding a free-kick, despite the contact seeming to occur inside the box.
The set-piece came to nothing and Ipswich's night was about to take a turn for the worse as Martin received his marching orders five minutes from half-time.
The winger was chopped down by Lansbury and the pair tangled as they got to their feet. Martin turned around and aimed his arm into the midriff of the former Arsenal midfielder, who promptly hit the deck, right under Webb's nose and a red card duly followed.
However, a difficult ask for Ipswich became nigh impossible when Webb gave Stearman a highly-questionable second caution in the 69th minute as he muscled Reid off the ball near the touchline.
Reid threatened to break their resistance when he teed himself up for a volley which Henderson tipped wide, and he was equal to McGugan's effort from the corner too.
McGugan's drive from distance struck an Ipswich player, sending it in to the bottom left-hand corner, with Henderson stranded, as Forest emerged from the thick fog with all three points.