Forest's ninth home win in succession was slightly harsh on the Teessiders, who were the better side for large parts of a tight first half.
However, Boro's inability to carve out chances eventually proved costly, and their play-off hopes are now hanging in the balance as a result of this defeat and Tuesday's reverse at Blackpool.
There was nothing to choose between the two sides in a tight first half, with Middlesbrough enjoying the lion's share of possession, but Forest carving out the better opportunities.
Radoslaw Majewski came within inches of giving the hosts the lead in the 13th minute, but while his 25-yard free-kick beat Boro goalkeeper Danny Coyne, it rebounded off the top of the crossbar.
Robert Earnshaw also went close before the break, racing on to Cohen's lofted through ball, only to loft his subsequent shot narrowly over the top.
Boro enjoyed plenty of the ball, with Gary O'Neil and Barry Robson combining effectively in midfield, but neither Scott McDonald nor Jeremie Aliadiere was able to carve out an opening.
Indeed, the visitors would have fallen behind midway through the second half had Danny Coyne not produced an excellent low save from Majewski's fierce drive. Robert Earnshaw pounced to tap home the rebound, but the Forest striker was rightly flagged offside.
There was no let off for Boro with 18 minutes left though as Forest produced the best passing move of the afternoon to break the deadlock.
Majewski fed Dexter Blackstock, he rolled the ball into Cohen's path, and the right midfielder steadied himself in the area before slotting a precise low finish into the net.
Boro's best chance of the game came in the 79th minute, but substitute Leroy Lita saw his fierce drive deflected narrowly wide after a deft lay-off from McDonald.
NOTTS FOREST (4-4-2): Camp; Gunter, Morgan, Wilson, Perch; Cohen, Majewski (Moussi 80), McKenna, Anderson (Adebola 89(; Earnshaw (McGoldrick 75), Blackstock.
Subs (not used): Chambers (gk), McGugan, Garner, Smith.
MIDDLESBROUGH (4-4-2): Coyne; Naughton, Wheater, McManus, Pogatetz; Flood, O'Neil, Robson, Arca (Franks 80); McDonald, Aliadiere (Lita 68).
Subs (not used): Steele (gk), Hoyte, Taylor, Grounds, Miller.