The hosts were dealt an early blow when Simon Church was forced off with a shoulder injury, but had the first effort of the game moments later when Gareth Bale tested Anastasios Kissas with a dipping free kick.
David Cotterill, sent on as a replacement for Church, broke the deadlock in fortunate fashion in the 13th minute when his dangerous cross evaded everyone inside the box before hitting the back of the net.
Wales continued to look threatening going forward, and the influential Bale was involved in his side's second goal 10 minutes later when his clever flick released Hal Robson-Kanu, who remained calm in front of goal to slot past Kissas.
However, a mistake from Wayne Hennessey brought Cyprus back into the game later in the first half as the Crystal Palace goalkeeper failed to deal with a Vincent Laban free kick which eventually crept in at the back post.
Kissas prevented Wales from restoring their two-goal advantage before the break by tipping a deflected Bale free kick against the crossbar.