Injuries and the ineligibility of some older players from the last campaign meant manager Stephen Robinson took an inexperienced squad to Nicosia's Makarion Stadium and they were comfortably beaten by their Group 9 opponents in baking conditions.
Onisiforos Roushias opened the scoring in the 19th minute and second-half strikes from Zacharias Theodorou and Pieros Sotiriou sealed the points for the home side.
Cyprus were on top from the start, Demetris Moulazimis hitting the woodwork inside the first three minutes before Linfield goalkeeper Ross Glendinning was forced into a smart follow-up save.
James Gray had Northern Ireland's first attempt after six minutes but could not find the target.
Glendinning made another good save in the 15th minute but had no answer four minutes later when Roushias struck the opener from Sotiriou's assist.
Gray had chances to level either side of half-time but missed both and Theodorou cashed in with Cyprus' second in the 59th minute.
Ten minutes later the result was in no doubt, Sotiriou converting following a corner.
Glendinning prevented the scoreline getting any worse but Northern Ireland's attacking efforts dried up the closing stages.