Forest secured a 3-2 win over their hosts at bet365 Stadium on Friday, which moved them to the summit of the Championship table.
Stoke City are yet to win a game this season and they are rooted in the relegation zone after picking up two points in nine league matches.
With both teams levelled at half-time, Ameobi linked up with Matthew Cash's cross to fire Nottingham Forest ahead, two minutes into the second-half.
At the end of the thrilling encounter, the 27-year-old forward who arrived at the City Ground on a free transfer this summer, was presented the Man of the Match award for his fine display.
Ghana's Albert Adomah was introduced as a 77th-minute substitute for the Reds while Ameobi and Mali's Samba Sow were on parade for the entire 90 minutes.
Stoke City will be hoping to pick up their first win of the season when they face bottom-placed Huddersfield Town on October 1 while Nottingham Forest travel to Blackburn Rovers for their next Championship fixture.