The pressure was on new head coach Roberto Martinez after his team were outplayed by Spain in a friendly last week, but it proved to be a comfortable night for the Spaniard on what was his competitive debut in the hotseat.
Belgium came close to moving 2-0 ahead five minutes before the break when Eden Hazard struck a powerful effort towards the bottom corner, but Panayi was on hand to make a smart save.
Eventually the second came for Martinez's side just past the hour as Lukaku again turned home from close range after Yannick Ferreira Carrasco had seen his effort pushed into the box by the home side's busy goalkeeper.
Belgium continued to dominate and scored their third in the 81st minute when Carrasco collected a pass from Hazard before finishing, but the visitors passed up the chance to make it 4-0 from the penalty spot late on as Michy Batshuayi saw his effort saved by a goalkeeper that faced 10 attempts on target in the 90 minutes.
Cyprus, whose best chance of the night fell to Dossa Junior on the hour, are next in Group H action away to Greece on October 7, while Belgium will host Bosnia-Herzegovina on the same night.