Forced to play a home match in Senegal because it does not have an international-standard stadium, Rwanda was on the verge of holding a team ranked 116 places higher in the world.
But Mane rescued the Teranga Lions on 98 minutes, with a hard, low penalty that eluded the outstretched hand of goalkeeper Olivier Kwizera.
Mane has starred in the first two matches for the title-holders, scoring four goals, including a matchday one hat-trick against Benin.
Despite the huge rankings gap, Senegal took no chances against the Rwandan Wasps, who have qualified for the Cup of Nations only once in 13 attempts.
Coach Aliou Cisse chose seven of the team that started the final victory over Egypt in Cameroon four months ago and introduced two more off the bench.
Mozambique, which began its campaign by drawing with Rwanda, could close the gap behind Senegal to two points by winning away to bottom team Benin on Thursday (AEST).
In Group H, Kings Kangwa rifled a free-kick into the net on 88 minutes to give Zambia a vital 2-1 victory over the Comoros in Lusaka.
Former African champion Zambia achieved success the hard way, coming from behind in a fast-tempo, foul-riddled regional showdown.
Serbia-based Ben Nabouhane took advantage of two defensive mix-ups to fire the visitors into a 13th-minute lead at a packed National Heroes Stadium.