Patrick Matasi's fine display kept Senegal at bay until the 63rd minute of Monday's Group C clash in Cairo, but Kenya's goalkeeper was at fault when Ismaila Sarr opened the scoring.
Kenya had gone close themselves shortly prior to Sarr's opener, with Alfred Gomis making a fine save from Dennis Odhiambo, but Mane – who had a poor first-half penalty saved – capitalised on slack defending to double the lead.
Philemon Otieno's ugly foul on Sarr handed Senegal another penalty and a numerical advantage soon after, with Mane making no mistake from the spot this time to add further gloss to a routine win which will please head coach Aliou Cisse, who had been angered by counterpart Sebastien Migne's pre-match suggestion that Senegal's players were mentally weak.
Victor Wanyama should have been penalised for a clear handball in the 19th minute, but Musa Mohammed's challenge on Saliou Ciss gifted Senegal a chance to make the breakthrough.
Mane could not take advantage, however, as his tame effort proved easy for Matasi to deal with.
But Kenya's resistance was finally ended after the hour when Matasi was caught out of position from Lamine Gassama's cross, and Sarr took full advantage with an acrobatic finish.
And any hopes of a comeback were ended when Mane raced clear of Mohammed to open his account for the tournament, before doubling his tally from 12 yards after Otieno picked up a second booking for a rash lunge on Sarr.
The result means Senegal, runner-up in the group behind Algeria, advances to a last-16 meeting with Uganda while Kenya must wait and see if it progresses as one of the best third-placed sides.