It was an eventful first-half with Alexander Mitrovic giving the home side the lead before a brace from Jason Cummings turned the game on it's head. Despite this, Rolando Aarons got his side back on level terms just before half-time.
However, Tyler Walker was then introduced by the away side in the latter stages of the game and his strike in extra-time was enough to secure his side's passage into the third round of the competition.
An entertaining first-half
As expected prior to kick-off, both Rafael Benítez and Mark Warburton made several changes to their starting line-up from the weekend with the league being a priority for both managers. However, both sides still looked reasonably strong considering the amount of changes that had been made.
It did not take long for the hosts to take the lead through Mitrovic who was handed a rare start. Rolando Aarons caused the Forest defence all sorts of problems right from kick-off and it was his cross that was turned in by Mitrovic to put Newcastle 1-0 up with only three minutes played. It was the ideal start for Benitez's side following a poor run of form.
However, despite going behind so early on, Forest continued to play their fluid style of football and began to create some opportunities of their own with the likes of Zach Clough, Ben Brereton and Cummings linking up well.
The away side scored a deserved equaliser on the half-hour mark as Clough's chipped cross into the area was headed into the back of the net by Cummings for his second goal since joining his new club to make it 1-1. The 22-year-old striker then wasted no time as he scored his second of the game to put his side 2-1 up just minutes later.
Danny Fox was given a chance to impress in the starting line-up by Warburton and his sublime pass played Cummings through on goal before he expertly lifted the ball over Karl Darlow in the Newcastle goal to give his side the lead.
However, despite an impressive first-half performance from Forest, they could not hang on to their lead till half-time. Newcastle caught the Forest defence off-guard on the counter attack and Aarons was on hand to fire his shot into the top corner from 20 yards out to make it 2-2 and send his side into the break on level terms.
Nothing to separate the two sides
It was the home side who again started the second-half looking the brighter of the two sides. Jacob Murphy joined Benitez's side from Norwich City this summer and he looked lively as Jordan Smith had to prevent his curling strike from finding the back of the net. Fox then had to produce an outstanding block to prevent Mohamed Diamé putting his side ahead from close range.
However, Forest did begin to come back into the match and create some chances to go ahead once again. Cummings was looking for his hat-trick and could have got it if he had kept his shot down following good play by Clough in the middle of the park midway through the second-half.
Newcastle had a huge opportunity to get themselves in front with little over 10 minutes remaining. Mitrovic dispossessed Joe Worrall in a dangerous area before Murphy wasted the chance by firing over the bar. It was a huge let off for Worrall who was caught off-guard by the Newcastle forward.
Tyler Walker replaced Brereton in the latter stages for the away side and he immediately made an impact. He did brilliantly to carry the ball from his own half to a dangerous area before being taken down by Grant Hanley. He then won his side a free-kick on the edge of the area from which Cummings hit the top of the crossbar with a great effort. This turned out to be the last opportunity before the game headed into extra-time.
Forest snatch victory in extra-time
Murphy had a great opportunity to put Newcastle ahead just five minutes into extra-time. However, substitute Jack Hobbs was able to put his body on the line and prevent his goal bound effort from finding the back of the net. It turned out to be a significant moment as Forest took the lead just minutes later.
Walker had made a huge impact since coming on as a substitute and he got a deserved goal in the first-half of extra-time to put his side 3-2 ahead. It was Hobbs who headed a corner back across goal and Walker was on hand to divert the ball past Darlow to give his side the lead.
The home side did have two great chances to get themselves back into the game before half-time in extra-time. Diamé somehow headed Matt Ritchie's cross over the bar from close range when he should have scored. Jesús Gámez then put in another great ball into the area but Henri Saivet could only fire wide.
The hosts had a couple of other opportunities to take the game to penalties in the final moments but they could not convert as Forest sealed their place in the third round of the competition for the second consecutive year.