Late Keane winner keeps Ireland on course
The visitors were spared their blushes when Keane caught the Cyprus defence off guard with a header in the 83rd minute.
Kevin Doyle had opened the scoring in the fifth minute, taking advantage of confusion in the Cypriot goal area.
But Cyprus equalised in the 30th minute with a long shot from Marios Elia.
The hosts were missing several key players and coach Angelos Anastassiades had to watch the game from the stands after being suspended for one match after being sent off in a previous home qualifier against Montenegro.
Ireland are now second in the group with 16 points, one behind Italy. Cyprus are fourth with five points.