The Nigerians had an early Semi Ajayi goal disallowed following a VAR review in this last-16 clash before the constant pressing and bullying of the Cameroon defence by Victor Osimhen led to Lookman finding the net in the 36th minute.
A team that has become impermeable at this AFCON then kept the Indomitable Lions at bay before Lookman made sure of the victory in the 90th minute in front of 22,085 fans at the Felix Houphouet Boigny Stadium in Abidjan.
They will now return to the same venue for a last-eight meeting next Friday with Angola, who earlier defeated Namibia 3-0.
"It was a big performance from the team, we fought well from the first minute to the 100th minute," said Lookman.
With the fearsome Osimhen leading from the front, the Super Eagles are clearly a serious threat to reigning champions Senegal as they chase a fourth continental crown.
"I am very happy with my boys. I think our team did a very good job against a very good team. We deserved to win," insisted Nigeria coach Jose Peseiro.
Meanwhile, Cameroon coach Rigobert Song said a lack of experience cost his side as they go home.
"I have a young team and players who are learning at this level," he admitted.
"They will learn and improve from their mistakes. In two or three years from now it will be the same players but a different team."
This fixture is a Cup of Nations classic, with the first three of Cameroon's five titles coming after wins over Nigeria in the final.
The very first, when a side led by Roger Milla came from behind to win 3-1 in 1984, was achieved in this same stadium in Ivory Coast's economic capital.
Yet Nigeria won the most recent encounter with their neighbours, in the last 16 in Egypt five years ago, and their current side came into this match as favourites.
The Super Eagles eased through their group unbeaten, while Cameroon needed a stoppage-time goal against Gambia to progress.
Their most recognisable name is Andre Onana, but the Manchester United goalkeeper was dropped for a second successive game, with Fabrice Ondoa of French third-tier side Nimes preferred between the posts.
Vincent Aboubakar, their skipper and main goal threat, was named among the substitutes after missing the group stage injured.
Nigeria brought back captain William Troost-Ekong, Lookman and Alex Iwobi –- scorer of the winner in that 2019 tie –- after all were rested for their last match against Guinea-Bissau.
Tireless Osimhen
Their pressing game caused problems for Cameroon from the off, and Nigeria thought they had taken the lead inside eight minutes.
A Moses Simon shot was saved by Ondoa but the ball broke to Ajayi and the West Bromwich Albion defender found the net despite the goalkeeper getting a touch.
Wild celebrations ensued, only for the Moroccan referee to come across to the VAR monitor and disallow the goal because Ajayi was deemed offside and interfering when the initial shot came in.
Not to be discouraged, Nigeria did not stop running, with the tireless Osimhen setting the example.
He provoked the opening goal, dispossessing Oumar Gonzalez after a throw-in had been played back towards the Cameroon defender, and then unselfishly setting up Lookman.
The Atalanta forward's shot was straight at Ondoa, but the goalkeeper could only help the ball on its way.
Osimhen slumped to the turf on the half-time whistle, but the African footballer of the year discovered the energy to go again after the restart.
Peseiro has stressed that the priority for his team has been to make sure they don't concede goals, and they stood firm despite having goalkeeper Stanley Nwabili stretchered off late on.
Aboubakar's introduction for Cameroon changed nothing, and Nigeria got the killer second just before the game moved into 10 minutes of injury time.
Calvin Bassey crossed low from the left and London-born Lookman applied the finish.
