In the second half, Nicolas Pepe added the third for Ivory Coast in the 54th minute to ultimately seal the win.
Captain Riyad Mahrez then missed a penalty but Sofiane Bendebka pulled one back for Algeria in the 73rd minute.
Ajax striker Sebastien Haller put the ball in the net but was ruled to be offside late on as Ivory Coast claimed all three points and top the group.
Algeria's AFCON title defense came to an end as they finished bottom of the group with no victories from three games.
The result was a shocker for Algeria as they crashed out of the tournament. The Desert Warriors as reigning champions were among the favorites to lift the title in Cameroon.
Not getting out of the group resulted in criticism of the team and star player Mahrez.
The 30-year-old winger is captain of the team and plays for Premier League giants Manchester City.
Mahrez did not score a goal in the competition and when provided the opportunity from the penalty spot could not convert.
His performance throughout the tournament was criticized by fans on social media.
While Algeria crashed out of the tournament, Ivory Coast await their round of 16 opponents for the knockout fixture scheduled on Wednesday, January 26, 2022.