Nathan Tyson's first goal for the club, as he rifled home in the 31st minute, was enough to give them a 1-0 victory, but the scoreline was not reflective of a match that the home side dominated for long periods.
But, despite the missed chances, the performance was enough to lift some of the pressure off under-fire boss Gary Megson, who had heard calls for his head from the terraces, following the weekend's 3-0 defeat at Chester – the third time this season that Forest had been defeated by lower league opposition in cup competitions.
Megson made three changes to his side and altered the formation and was
rewarded with a positive display.
Forest began the stronger side, as they demonstrated the confidence they are so badly lacking away from home, where they have won only twice all season.
But while they played the better football and carved out several half chances, with Ian Breckin putting a header wide from a corner and Nathan Tyson hitting a shot on the turn that lacked the power to trouble the keeper, it was Vale who enjoyed the more clear cut opportunities.
Nicky Eaden had to defend well as Leon Constantine looked to have broken clear of the Forest back line, only for the full-back to make up vital ground and prod the ball out for a corner.
Nathan Lowndes then squared a dangerous ball across the face of goal for the on-rushing Jeff Smith, but the winger saw his shot, from just inside the box, well saved by Paul Gerrard.
Forest continued to play some neat passing football and one such move was almost finished off in style, as Eaden fired in a deep cross from the right towards the near post, where Tyson was only denied by a superb interception from George Pilkington.
But their dominance was to pay off, as they this time probed down the left through teenager Felix Bastians, who found room to play a neat ball into the feet of Tyson, who had his back to goal ten yards out.
Tyson had been denied a goal on his Forest debut against Southend, when it was decided his strike had been deflected in off the boot of defender Jamal Campbell-Ryce, but there was no doubt this time, as he turned superbly before striking a low shot across the face of goal and into the bottom corner of the net.
Bastians, the German 18-year-old, was looking effective on what was his league debut for Forest, repeatedly finding room to cross from the left.
It was a theme that continued after the break, with two Bastians crosses causing havoc in the Vale defence, with the first being spilt by keeper Goodlad and the second somehow managing to elude both Taylor and Southall at the far post.
Vale were still a threat too, however, and Breckin had to produce a fine block when a corner broke to Pilkington around the penalty spot, after Gerrard had failed to properly clear, from where the striker struck a firm shot that seemed goalbound before the defender's interception.
Wes Morgan almost put Forest further ahead with a spectacular volley, hit on the turn, which flew narrowly wide, while Taylor could have done better with a free header, from ten yards out, which he directed wide of the post.
Tyson's confidence was clearly high, as he came close to scoring a goal out of nothing, with a 30 yard shot that floated inches over the angle of post and bar and then broke from a Vale corner, carrying the ball the length of the pitch before being denied by a last-gasp tackle from Craig James.
But, despite a late free kick from Tony Dinning, that Gerrard saved smartly, Forest were deserving of their eighth home success of the campaign.