The striker, who has been out of favour at Chelsea for much of the season, powered home a header from just inside the penalty area in the 60th minute to settle a match containing few scoring opportunities.
Kalou also netted in Abu Dhabi on Friday when the Ivorians looked more convincing in a 2-0 win over Tunisia.
New African Footballer of the Year Yaya Toure was back in action on Monday after he missed the Tunisia game through injury.
The Ivorians launch their Nations Cup campaign against Sudan on Sunday.
Libya play in the opening game against co-hosts Equatorial Guinea on Saturday.
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