Craig James' cross from the right provided Leon Constantine with the opportunity to shoot after only five minutes but his acrobatic overhead kick was saved well by stand-in goalkeeper Rune Pedersen.
The Valiants continued to carve out opportunities and on nine minutes Sam Togwell took advantage of a half-clearance by Wes Morgan, firing a low drive inches wide from 20 yards.
Togwell threatened the away goal again in the 14th minute, but his header from Chris Birchall's cross beat the goalkeeper but not the crossbar.
Forest eventually broke Vale's stranglehold on the game after 24 minutes when James Perch was allowed room to run and shoot from 30 yards but his low drive skipped past Mark Goodlad's right post.
The deadlock was broken five minutes before half-time when former Stoke City player Kris Commons stepped up to flight a 25-yard free-kick over the Vale wall and past the helpless goalkeeper.
Nathan Lowndes found his shooting boots after the restart and was unlucky not to get onto the scoresheet when he found room out on the left to fire a testing shot into Pedersen's gloves.
Goodlad was called into the action again in the 68th minute when Wes Morgan met Commons' corner but the shot-stopper got across well, parrying the ball away.
Vale were left cursing their luck again six minutes before the final whistle when Lowndes got the slightest of touches on a pacy James cross but the ball drifted just wide.
Vale were caught napping at the back in the dying seconds when Nathan Tyson was released by Jack Lester, confidently rounding Goodlad and slotting into an empty net to give his side the points.