Denmark keep qualification hopes alive
Halftime substitute Morten Rasmussen headed home the opener three minutes into the second period.
Rasmussen was denied a second by Cypriot keeper Antonis Georgallides soon after and Dennis Rommedahl had a goal ruled out for offside.
Cyprus also had their chances before Kasper Lorentzen sealed victory for the Danes nine minutes from time.
Denmark have six points from three matches. Norway top the group on nine points with Portugal, playing away against Iceland later on Tuesday, on four.