Eto'o matched the record of Ivory Coast's Laurent Pokou as former Middlesbrough forward Joseph Desire Job netted twice.
Geremi Scores In 5-1 Win!
Cameroon took the lead after 28 minutes when Newcastle's Geremi curled a free-kick over the wall.
Cameroon added the second when two Zambia defenders failed to clear a long ball up field and Job was presented with an easy chance.
Achille Emana scored the third after 44 minutes and then Eto'o saw his free-kick strike the hand of by Billy Mwanza in the 65th minute and scored from the penalty spot.
Job had a simple tap-in for the fifth with 10 minutes left before Chris Katongo volleyed a consolation goal for Zambia in the 89th minute.
Defending champions Egypt, who had beaten Cameroon 4-2 in their opening fixture, defeated Sudan 3-0.