Victory at Peterborough on Saturday would be enough to secure promotion if third-placed Forest, who have now lost their last eight away games, extended that to nine at Bristol City with the Magpies 13 points better off having played a game fewer.
It was Ameobi's first appearance since February 9 and his first goal since Boxing Day, but it was arguably the most important of his nine for the season to date.
The game kicked off in torrential rain which made conditions underfoot treacherous for both sides, and it was the visitors who coped the better during the early stages.
Newcastle created the game's first chance when Carroll thumped in a firm volley from Wayne Routledge's cross to force goalkeeper Lee Camp into a good 12th-minute save.
As the half wore on, the Magpies began to dominate the midfield battle, and Carroll might have done better in the midst of a 24th-minute goalmouth scramble, but he could not get his shot away after good work by strike-partner Peter Lovenkrands and Jonas Gutierrez.
Routledge saw a shot blocked by Kelvin Wilson five minutes later with the visitors pinned back inside their own penalty area, but his side had a let-off 13 minutes before the break.
Nathan Tyson turned up on the left to pick out striker Dexter Blackstock with an inviting cross, but he miskicked in front of goal.
Lovenkrands could not get a decisive touch amid another melee after Gutierrez's 44th-minute cross caused panic in the Forest box, and Jose Enrique whistled a long-range effort across the face of goal seconds later.
Tyson headed weakly at Newcastle keeper Steve Harper within a minute of the restart after midfielder Paul Anderson crossed from the left as the visitors made a good start to the half.
The game was becoming increasingly scrappy as both sides continued to seek a breakthrough, but it took a good block from Fabricio Coloccini to deny Anderson after he broke from halfway with 59 minutes gone.
Danny Guthrie curled a free-kick high over two minutes later and Forest started to make their big push.
But it was the home side who eventually went ahead with 19 minutes remaining when Ameobi received Kevin Nolan's pass with his back to goal and turned smartly before firing a low left-foot shot in off the far post.
Routledge might have sealed the win with 15 minutes remaining, but saw his stinging effort palmed away by Camp, who then produced fine stops to deny Nolan and Guthrie.
However, Enrique's first goal for the club in injury time sealed the win.