Forest had thrown everything at their promotion rivals but could not make the breakthrough in front of a crowd of more than 28,000. And Carlisle - who scored with their only shot on target - were able to hold out for a win that put them in the driving seat in the race for second place.
Carlisle's former Notts County defender, Danny Livesey, almost made an early impact with a looping header that dropped just wide of the post, while Graham also glanced an effort narrowly the wrong side of the upright for the visitors. But it was Forest that were enjoying the majority of the possession, playing at a high tempo.
They were almost rewarded when a flowing move down the left flank guided Julian Bennett into space on the edge of the box, from where he delivered a pacy ball towards the near post for Junior Agogo, the Ghana striker forcing a smart save with an instant shot. Agogo's physical presence was also creating openings, particularly for Kris Commons, who he teed up for chances three times in the space of five first half-minutes.
Commons' first, a driven shot from the edge of the box, was always flying wide, after Agogo had headed the ball down. A second, when the ball had been half-cleared by the Carlisle defence as Agogo powered forward, was well saved by Keiren Westwood. But when Agogo flicked the ball into his path for a second time, this time as he rampaged into the box, Commons came agonisingly close as he tried to place a shot into the bottom corner.
A Commons corner almost provided the breakthrough, as he picked out Bennett, who saw his powerful header superbly palmed over by Westwood. It seemed only a matter of time before Forest would score as Commons had a looping header cleared off the line and Grant Holt powered a shot over following good work from Agogo and Chris Cohen.
But the half-time interval gave Carlisle the chance to regroup and it became a more tightly-fought contest after the break. Marc Bridge-Wilkinson could have snatched the lead for the visitors, but failed to connect with a ball whipped right across the face of goal.
But it was to be a cruel mix-up between keeper Smith and defender Kelvin Wilson that handed the visitors a goal they never looked like engineering on their own. As a deflected ball bounced into the box, Wilson appeared to step aside to allow Smith to collect, but he failed to claim and left Graham with the task of sliding the ball into the exposed net.
Commons went in search of an equaliser with a lashed low shot that was blocked on the line, with Agogo sweeping the rebound towards the far corner, where it was again cleared on the post. It then took a breathtaking stop from Westwood to thwart Commons after he sent a vicious 25-yard free-kick bending towards the top corner.