Captain Vincent Aboubakar and Karl Toko Ekambi both scored twice as Cameroon turned in a strong second-half performance and advanced to six points after also winning their opening game against Burkina Faso.
But the triumph over Ethiopia at the Olembe Stadium was more convincing and will come as a morale boost as they carry a major burden of expectation.
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Ethiopia made a shock start as they caught Cameroon's defence napping, with Amanuel Aregawi delivering a square ball into the area and Dawa Dukele getting in front of his marker to slot home the pass.
It was the second time Cameroon trailed in the tournament, but they needed only four minutes to equalise. Collins Fai, who had proven slovenly in defence when Ethiopia scored their goal, made amends with a quality cross and Toko Ekambi took advantage of poor marking to head home in the eighth minute.
The French-born striker then rattled the woodwork with a header, but Ethiopia were also dangerous on the counter-attack, catching out Cameroon repeatedly with their pace even if they did not have much possession.
But the underdogs wilted soon after the start of the second half as Aboubakar scored twice in as many minutes. He headed home Collins's cross in the 53rd minute, then slid home a similar square ball from Nicolas Moumi Ngamaleu.
Toko Ekambi scored his second, and Cameroon's fourth, in the 67th minute.
"We were mentally ready for this game. This is a big boost for the tournament and we hope we have more spectators for our next game," he told a news conference.
COVID restrictions meant the newly built Olembe Stadium was around 20 percent full for the match.
Burkina Faso and the Cape Verde Islands meet later on Thursday in Group A.