Yaya Toure crowned a towering performance with an 87th-minute goal after Gervinho had given the Ivorians the halftime lead and Didier Ya Konan added the third just seconds after coming on as a substitute.
It was a marked improvement on Tuesday's limp start when the Ivorians needed a late goal to beat Togo 2-1 in their first match of the tournament.
Captain Didier Drogba was dropped for the first time, although he came on for the final 25 minutes, and Kolo Toure was also left out by coach Sabri Lamouchi as he attempted to kick-start the campaign for the much-fancied Ivorians.
The victory means the Ivorians, the only side in the competition with a 100 percent record, could be the first team through to the knockout stage if the second Group D match at the Royal Bafokeng Sports Palace between Algeria and Togo does not produce a winner.
"This is really the start of the tournament. I'm very satisfied with my players and their reaction. How we played is a reflection of what we have been working on in training," said coach Lamouchi.
But he did not directly address questions about the talismanic Drogba being dropped to the subs bench.
"Those who were fielded were the ones who I believe were ready to face Tunisia from the first minute of the game. I don't see great players, only a great team."
Gervinho finished off an audacious interchange of passes with Lancina Traore in the Tunisian box to score the first goal in the 21st minute at the end of a sustained period of pressure.
It took until the final three minutes for the Ivorians to add more. Toure, playing a more forward than usual and revelling in his new role, got a superb second with a shot from just outside of the penalty box.
Ya Konan had just a couple of touches before he tucked away the third in the 90th minute from almost the same position as the Ivorians stormed all over the Tunisian defence.
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