Michael Morrison’s 87th minute header ensured a nervous finish, on an afternoon when Reds keeper Costel Pantilimon had to make some important saves to hold the Blues at bay.
That was Birmingham’s first goal in five Championship matches, but it was not enough to prevent a fifth straight defeat, as goals from Joe Lolley and Matty Cash, either side of half-time, helped Forest notch up a fourth game unbeaten, to put a bit of breathing space between them and the bottom three.
But Birmingham remain in the relegation zone and Cotterill will continue to face questions about his future.
It took Forest only six minutes to take the lead, after Lolley had collected a ball from Lee Tomlin, before advancing powerfully toward the edge of the penalty area, where some clever footwork gave him the room to find the bottom corner with a crisp shot, albeit with the aid of a slight deflection.
Forest had a let-off when Jacques Maghoma cut a dangerous ball back into the area from the right, picking out Maikel Kieftenbeld, who skied his shot well over.
Harlee Dean had another chance to level from a free-kick, but guided his angled effort the wrong side of the post, as Forest appealed for an offside decision that never came.
Forest looked to add more attacking threat by replacing the youthful Ben Brereton with the experienced Daryl Murphy up front at half-time.
It was Cash who almost scored six minutes into the second half when he hammered a rising shot from 14 yards that looked to be bound for the net, until bouncing away off the underside of the bar.
Within a minute, David Stockdale had to make an adept save to push away a crisp strike from Tendayi Darikwa. Murphy was next to threaten as he flicked across goal and wide, following a low cross from Cash. Jack Colback then had a shot held by Stockdale at the second attempt.
Birmingham sub Lukas Jutkiewicz also forced an awkward save from Pantilimon with a long-range effort.
Forest gave themselves some breathing space with 11 minutes to go, as Ben Osborn’s cross-field pass found Cash in space on the right. His first touch was good, but his next one was better, as he applied a precise finish from just inside the box, sending a low shot across goal and inside the far post to make it 2-0.
When Craig Gardner delivered a corner towards the far post, Morrison rose to power home a header and give Birmingham late hope with three minutes to play.
Another corner caused panic in the Forest defence, with Ben Watson sending an attempted clearance spinning towards his own net, but Pantilimon held on – and so did the home side.
Morecambe have no fresh injury concerns ahead of Tuesday's Sky Bet League Two home clash with Colchester.