Three-time winners Nigeria scored the only goal in the 73rd minute when Moses Simon's right-wing corner was headed in at the near post by Kenneth Omeruo.
They now have six points from their two games after a 1-0 win over Burundi in their first match on Saturday.
The top two nations in each of the six groups advance, along with the four best third-placed countries.
AFCON 2019 Group B
|Nigeria - WA||6||4||0||2||8||7||12|
|Madagascar - IO||5||2||2||1||7||7||8|
|Guinea - WA||4||1||1||2||4||6||4|
|Burundi - EA||3||0||0||3||0||4||0|
|Nigeria - WA||1||-||0||Burundi - EA|
|Alexandria – 22nd June 2019 6:00 pm|
|Guinea - WA||2||-||2||Madagascar - IO|
|Alexandria – 22nd June 2019 9:00 pm|
|Nigeria - WA||1||-||0||Guinea - WA|
|Alexandria – 26th June 2019 3:30 pm|
|Madagascar - IO||1||-||0||Burundi - EA|
|Alexandria – 27th June 2019 3:30 pm|
|Burundi - EA||0||-||2||Guinea - WA|
|Cairo – 30th June 2019 5:00 pm|
|Madagascar - IO||2||-||0||Nigeria - WA|
|Alexandria – 30th June 2019 5:00 pm|
Watch Nigeria vs Guinea 1-0 All Goals Full Highlights
Nigeria dropped captain John Mikel Obi, who played for Middlesbrough in 2018-19, but their side did include Brighton defender Leon Balogun, Stoke midfielder Peter Etebo, Leicester midfielder Wilfried Ndidi and Arsenal forward Alex Iwobi.
The Gunners man had one of the best chances when it was goalless with a curled effort from just outside the penalty area, but Guinea goalkeeper Ibrahim Kone produced a spectacular one-handed save to push it over the bar.
Guinea's side included Liverpool midfielder Naby Keita, who was making his first start for club or country since 1 May, when he picked up a groin injury in the Reds' 3-0 loss to Barcelona in the first leg of their Champions League semi-final.
However, Keita received some strong challenges and only lasted 71 minutes before he was substituted.
He was replaced just before a Nigeria corner and Guinea, who now have one point from their two matches, went behind instantly thanks to Omeruo's header.
The other two nations in Group B, Madagascar and Burundi, play on Thursday (15:30 BST), before Burundi take on Guinea and Madagascar face Nigeria in the final round of group games on Sunday.
BBC World Service's John Bennett
They say it is a sign of a good team if you win without playing at your best. That is twice now that Nigeria have got the job done despite not hitting the heights.
There is plenty more to come from the Super Eagles and some real quality on the bench.
Guinea huffed and puffed but it's tough for them at this tournament with their star man Naby Keita half-fit. He was running on empty today at times but showed glimpses of what he can do towards the end of the first half.
Now the next challenge for Nigeria is finally sorting the bonus row. The players are expecting to receive the money on Friday. Then it would be all resolved and they can fully focus on the football.
Kenneth Omeruo is registered as a Chelsea player but has had seven loan spells away from the club, including two with Middlesbrough