Cotterill had won both of his opening two matches since succeeding Steve McClaren but Mclean's second-half strike maintained Hull's impressive away form and moved them into the Championship play-off places.
Former Forest captain Paul McKenna was the architect, providing the pass from the right for Mclean to net his third goal of the season.
Cotterill's men struggled to create clear-cut chances against a side that has now lost just twice on the road in 25 league matches stretching back to last October.
Greg Cunningham made his Forest debut. Cunningham joined the Reds on loan from Manchester City this week and lined up at full-back.
That saw Joel Lynch pushed forward on to the wing as Jonathan Greening moved into central midfield to cover the absence of the suspended Guy Moussi, who was sent off during the win at Blackpool last weekend. Hull were unchanged.
Radoslaw Majewski and Marcus Tudgay threatened early on and Lewis McGugan went close with a free-kick. Lynch headed wide from a McGugan corner midway through the first half.
Almost immediately at the other end, Lee Camp made a routine save when Tom Cairney tried his luck from long range.
McGugan shot over before providing a cross that Wes Morgan headed straight at Adriano Basso.
Robert Koren worked Camp again from long range just before the hour mark.
Basso produced the first meaningful save of the game after 64 minutes, tipping a 25-yard effort from Majewski round the post.
Soon afterwards, Majewski whipped in a free-kick and Ishmael Miller headed wide.
Matty Fryatt, who scored the winning goal for Hull in this fixture last season, was the next City player to have a shot from long distance. And like those before him, he failed to trouble Camp.
Substitute Dele Adebola caused his former club problems following his introduction from the bench just after the hour and the big Hull striker sent a low shot narrowly wide midway through the second half.
Mclean latched on to McKenna's pass in the 74th minute to beat Camp from close range.
It proved to be the decisive strike as Forest failed to muster a response.