Senegal fielded a full-strength side, with Mane leading the attack, but had to wait until a minute before the final whistle to secure the win over the No. 136-ranked team in their Group L clash at Dakar's new stadium.
Senegal were supposed to play their match in Kigali but renovations to the stadium in the Rwandan capital saw the two associations agree to switch around their qualifiers, so that Rwanda will host Senegal at the end of the qualifying competition next March.
Senegal had begun the defence of the Cup of Nations crown that they won in February with a 3-1 victory over Benin in Dakar at the weekend, when Mane scored a hat trick, including two spot kicks.
But this time there was only a last-gasp penalty for the large crowd to cheer, after a clumsy challenge from Jimmy Mutsinzi on Saliou Ciss ended Rwanda's hopes of pulling off a remarkable result.
Kings Kangwa slotted home a dramatic curling free kick two minutes from time to hand Zambia a narrow 2-1 win over Comoros Islands in Lusaka in Group H after they found themselves a goal down after 13 minutes when a defensive mixup allowed the Red Star Belgrade striker El Fardou Ben Nabouhane to snap up the loose ball and strike firmly into the net.
Zambia captain Enock Mwepu equalised just before halftime before Kangwa won the game.
Eswatini, who had held Togo away at the weekend in their opening Group B match, went ahead after 64 minutes in Johannesburg against Burkina Faso but then saw their work undone in the space of six minutes when 20-year-old Dango Ouattara scored twice for the Burkinabe as they went on to win 3-1