Igor Lolo sent a cross toward Kalou who headed it past keeper Samir Abod in the 63rd minute. The goal followed relentless pressure from the African Cup of Nations favorites. Nine minutes earlier, Hannover striker Didier Ya Konan's close-range header was swatted away by a diving Abod.
In the first half, Kalou's Chelsea teammate Didier Drogba hit the post from long range in the 32nd minute.
Libya, a surprise qualifier for the tournament which kicks off Jan. 21, was outplayed most of the match. Its only serious threat came in the 73rd minute when substitute Ahmad Saad got past the defense but fired his shot wide left.