The victory - earned by Brett Ormerod's second goal in two games since being signed on loan from Preston and a controversial second-half penalty by Nathan Tyson - condemned the Cobblers to only their second defeat in 14 games and a first at home in almost four months.
As well awarding the contentious match-winning penalty, the major talking point of the match was the 20th minute dismissal of Forest centre-back James Perch for a 'studs up' challenge on Poul Hubertz which instantly saw Styles brandishing a red that caused a furore which saw two visiting players booked for dissent.
Forest were already ahead at this stage thanks to a brilliant ninth minute strike from Ormerod who pounced to sweep home a cross by Chris Cohen after he had been released down the left by Julian Bennett.
Forest's pace and class was nullified after the dismissal and the home side were on terms in the 32nd minute when a long throw from Andy Holt resulted in a flick-on and a clinical overhead kick by Hubertz which crept inside Paul Smith's right-hand post.
If Northampton thought they were in for an easy ride against ten men their illusions were quickly shattered after the restart when Sammy Clingan blasted a 20-yarder against the underside of the bar and the visitors, with the wind at their backs, controlled the contest despite their player deficit.
But the key moment arrived in the 62nd minute when Mark Bunn was adjudged to have brought down Tyson, even though he emerged from the challenge with the ball in his hands.
Tyson duly converted the spot-kick but disappointed home boss Stuart Gray said after the match: "I only have to look at the reaction of my players to know that it wasn't a penalty."