The Canaries now sit on 82 points with only nine games left to play and there now is clear breathing space between them and second-placed Watford meaning that promotion back to the Premier League is looking ever more likely.
Meanwhile, for Forest, the prospect of relegation is still not over as despite being nine points away from the drop zone, 22nd placed Rotherham United do have four games in hand on Chris Hughton's side.
Story of the match
The visitors made a great start to the game as in the opening stages they dominated almost all of the possession and were a whisker of away from taking the lead, but Dowell's powerful effort from range flashed narrowly wide of the right-hand post.
The Canaries continued to pile on the early pressure with Hughton's side having all of his men sit behind the ball and on nine minutes Jordan Smith was forced into his first stop as he tipped Max Aarons low drive around the post.
However, only a minute later Daniel Farke's side did take a deserved lead when Pukki created himself space just inside the area and his low strike was fired past Smith and into the bottom left-hand corner.
Things got even better for Norwich only four minutes later as after a neat one-two with Lukas Rupp, Dowell fizzed the ball first time into the bottom hand corner once again leaving Smith with absolutely no chance.
In an electrifying start to the game, Ryan Yates had a golden opportunity to halve the deficit just after the quarter of an hour mark when he was found unmarked from a corner but his powerful header was glanced just wide of the far post.
The hosts had another chance from a corner eight minutes later with Tobias Figueiredo this time heading off target from a Luke Freeman delivery.
With the league leaders having a clear grasp they really should have extended their advantage when Todd Cantwell slipped in Pukki down the left-hand side but his first time shot nestled the side netting instead of the back of the net.
With 11 minutes of the half remaining, the away side created another gaping opportunity to get a third when Cantwell fed Kenny McClean inside the area, but his low shot was well kept out by the feet of Smith.
After the break, despite Norwich seeming to continue where they left off in the first period in the 50th minute the home side created their best opening of the game when Freeman worked a bit of room on their left-hand side but his powerful shot was fired just wide of the far post.
Three minutes later, Lewis Grabban should have found a route for Forest to get back into the game when on the break, he was slipped in by James Garner, but Tim Krul rushed out to close down the striker and consequently was there to block the hosts number seven's shot.
Just before the hour mark, Pukki who was looking for his second of the game and his 23rd league goal of the season, did well to speed into the area, but his low sliding shot from a tight angle was once again kept out by the feet of Smith.
Four minutes later, Farke's side broke away quickly once again with Pukki being found on the right-hand side, he made a cutback to the unmarked Cantwell but his effort was scuffed as it dribbled wide of the target.
With the games approaching the 75th-minute mark Pukki had yet another chance to claim a brace when he was found in space in the area by Dowell, but this time his well-struck strike was well blocked to safety.
The visitors even late on continued to fight for a third goal and full back Dimitri Giannoulis was the next one to try to get it, but his low shot inside the area was guided narrowly adrift of the right-hand post.
Even though the away side did have opportunities to add more to their tally, the damage had already been done in the opening stages as Farke's side cruised to a comfortable three points.
Promotion within Canaries reach now
Following this comfortable victory which is a ninth in a row for Norwich, it now means that they only need 12 points to seal promotion and only a further 17 points to lift the title.
With this being the case it means that it would take something majorly to go wrong if they were not to at least earn promotion back to the Premier League considering the healthy position they currently find themselves in.
If they did get promoted it would mean that Norwich have earned immediate promotion back up to the top flight and there will, of course, be a concern that like last season, Farke’s side will just jump straight back down to the Championship.
However, what must be beared in mind is that at this stage of the season during the 2018/19 campaign when they were crowned champions, they possessed 75 points.
As things stand now, they are seven points better off while also having lost a game less, something that when Norwich do earn their inevitable promotion will provide Canaries fans with hope and confidence of survival.
Forest’s lack of threat a worry
It is well known that going forward this season Forest have not been the most threatening as before this game they obtained the fifth-worst goalscoring record after only having netted on 29 occasions.
Then following this result tonight, their performance on the attacking side of things provided justification to why they have been so poor when going forward this season.
Throughout the entirety of the 90 minutes they failed to create much in terms of goalscoring opportunities and Krul really did not have much to be concerned with.
In fact, he only was forced into one crucial save from Grabban which arguably should not have even got to that point as Oliver Skipp felt that he should have been rewarded a free kick in the build-up to the opportunity.
For the remaining games of the season, Hughton’s side will have to make sure that they look more dangerous and threatening when going on the attack especially when they come up against the likes of the struggling Huddersfield Town, Birmingham City and Sheffield Wednesday.
If they do fail to do this though, especially with Rotherham United’s games in hand on Forest, they could find themselves being in serious danger of making the step down to League One.
Star Man- Lukas Rupp
Despite not managing to get on the scoresheet himself, Rupp proved to be excellent throughout especially in how he was the catalyst of everything good there was going forward for the away side.
His deft first touch and his quick feet caused the Forest backline problems defensively as it was clear that they did not know how to deal with the attacking midfielder.
Also, his decision making this evening was spot on as he knew exactly when it was the right time to play the ball in behind the backline and of course, he claims the assists to both of his side’s goals.
He further on a number of occasions in the second half was seen to slip in dangerous forward Pukki, but he was just unable to provide the finishing touch which ultimately would have made a very humiliating night for the Reds