The win now takes Nigeria back to the top of Group F with 8 points while Malawi are second on six after battling to a 0-0 draw with Namibia in a match played in Blantyre earlier on Wednesday.
Kenya, who had win to keep alive their hopes of gracing the World Cup final, started the match badly with defender Brian Mandela almost handing the visitors a quick goal in the 1st minute of the match.
The South African-based defender failed to deal with a loose ball after restart allowing Nigerian striker Brian Ideye to charge forward but the Super Eagles' star could not find the back of the net with keeper Ochieng’ to beat.
Five minutes later, Musa Ahmed beat the Kenyan defense but his attempt to pick out an advancing Sunday Mba was blocked by Brian Mandela.