The visitors had already gone close through Marek Matejovsky, Tomas Galasek and Michal Kadlec before midfielder Pudil, found the bottom corner of Antonis Georgallides' net from around 30 meters out.
Sverkos, playing only his fourth game for the Czechs, reacted quickest as the ball was headed back into the danger area by Tomas Galasek and volleyed home the 70th minute opener.