It had taken a Nathan Tyson strike in first-half injury-time to pull the home side level, after a Julian Bennett own goal had given the visitors a eighth-minute lead.
But after the interval it was one-way traffic and only a string of saves from Brown prevented Forest from claiming a comfortable victory.
Gillingham may have had a striker crisis with several players out injured and suspended, but it counted for little as Forest helped them into an early lead.
Midfielder Danny Spiller - playing as a makeshift frontman, found the room to dart into the box down the right hand side and cross dangerously into the middle.
Forest keeper Rune Pedersen failed to deal with the threat, as he allowed the ball to fly through to the far post where Bennett mis-hit an attempted clearance into the back of his own net, off the inside of the post.
The goal came after only eight minutes, but was not against the run of play as the visitors belied their previous run of three straight defeats with a positive start.
It took Forest 10 minutes to muster a meaningful reply. But when they did, it almost saw Gillingham concede an own goal at the other end, as James Perch latched onto the end of a Tyson flick-on and struck a low, but wayward, shot from the right side of the box, which took a nasty deflection off Ian Cox, forcing a decent save from Jason Brown as the ball looped dangerously towards the top corner.
Gillingham should have doubled their advantage when Justin Cochrane arrowed in a cross from the right to pick out Mike Flynn's run into the box, from where he planted a free header right at a grateful Pedersen.
Forest had a golden opportunity of their own as Tyson outstripped the Gillingham defence down the right and cut back a perfect ball for Kris Commons, who failed to make contact when faced with an open goal six yards out.
His blushes were spared within a minute, when he played in Tyson down the left-hand channel. The striker's initial effort was well saved by Brown, but the keeper could do little as the Forest man lashed the rebound under his body and into the back of the net.
Forest almost went ahead after the break as they stepped up a gear and took complete control of the match.
But Brown reacted superbly to deny Tyson a second and then regained his feet quickly to palm Grant Holt's shot from the rebound round the post.
Bennett almost made amends for his own goal with a fine solo effort which saw him beat two down the left before hammering a shot towards goal that Brown again saved, at the expense of a corner.
Clingan's ball to the far post picked out Bennett, who headed dangerously towards the near post, where Ian Breckin's headed effort was somehow cleared off the line by Sean Clohessy.
At this stage, Gillingham keeper Brown was under siege, as he made fine saves to deny Perch, Commons and Holt, in a 10-minute spell in which Forest dominated entirely.
But the visitors held on for a valuable point in their fight to avoid getting sucked down into League Two.