The Indomitable Lions almost snatched victory towards the end but Guinea keeper Ibrahim Kone made a fine save from Karl Toko Ekambi to ensure honours ended even.
The draw leaves both sides with work to do to qualify for the knockout stages with holders Senegal sitting top of Group C after their comfortable 3-0 victory over The Gambia earlier on Monday.
It was also another surprise outcome at the tournament in Ivory Coast after Ghana were upset by Cape Verde on Sunday while Egypt and Nigeria were held by Mozambique and Equatorial Guinea respectively.
Cameroon miss Aboubakar more than Onana
Cameroon were without two of their big names at the Charles Konan Banny Stadium in Yamoussoukro - injured captain and striker Vincent Aboubakar and goalkeeper Andre Onana.
The Manchester United stopper delayed his arrival at the competition to play for the Red Devils against Tottenham in the Premier League on Sunday - but his replacement Fabrice Ondoa had very little to do.
Ondoa saved well from Bayo initially in the build-up to the opening goal, but the Guinea striker nutmegged him at the second attempt after Olivier Kemen failed to clear the danger.
But it was Aboubakar - winner of the Afcon Golden Boot in 2021 with eight goals - who Rigobert Song's side clearly missed most, given how little they made Ondoa's opposite number Kone work.
Boosted by Kamano's clumsy dismissal - a yellow card upgraded to red after the video assistant asked referee Ibrahim Mutaz to consult the pitchside monitor - they did craft a fine leveller via Nkoudou's pinpoint cross and Magri's header.
However, Toko Ekambi's late effort was their only other shot on target and Cameroon now face a vital, yet daunting, second group match against Senegal on Friday they can ill afford to lose.
Guinea were also robbed of their talisman with a thigh problem sidelining Serhou Guirassy, the Bundesliga's second leading scorer this season, behind Harry Kane.
But they coped much better in his absence than Cameroon did without Aboubakar, Mouctar Diakhaby unlucky to see an early header float over before Bayo's opener.
Sekou Sylla almost lobbed Ondoa from 40 yards, and although the red card limited their attack in the second half, they will fancy their chances of progression with The Gambia next up, also on Friday.