There were also wins for South Africa, who edged Benin 2-1 at home in Durban, and Tanzania, who won 1-0 away to Niger.
Mane, twice African Footballer of the Year, set up the opening goal in the first minute for Pape Matar Sarr and grabbed one himself five minutes later, with veteran midfielder Idrissa Gana Gueye the provider.
A third Senegalese goal followed on the stroke of half-time of the Group B match in Dakar as 19-year-old debutant Lamine Camara stole the ball off the visiting defence on the edge of the penalty area and hammered home.
The 31-year-old Mane, who made his debut for Senegal in 2012, added the fourth from the penalty spot 12 minutes into the second half before being replaced after 63 minutes to stay fresh for the next qualifier in Togo on Tuesday.
Senegal are looking to qualify for their third World Cup in a row and are heavily fancied in the group, where the Democratic Republic of Congo should be their toughest opponents.
South Africa went top of Group C after scoring early but making heavy work of securing victory over Benin.
Percy Tau put them ahead in the second minute and Khuliso Mudau struck after poor Benin defending to make it 2-0 at halftime but Steve Mounie pulled one back to ensure an anxious finish for the hosts who have not been to the World Cup since hosting the 2010 tournament.
Australian-based striker Charles M'Mombwa scored in his first game for Tanzania as they beat Niger in neutral Marrakech, Morocco in Group E.
He fired home a deflected shot to strengthen his chances of being selected for January's Africa Cup of Nations finals in the Ivory Coast.
Niger are among the 19 African countries forced to move their home qualifiers to neutral venues because of poor facilities or security concerns.