Midfielder Andy King was given a straight red for a reckless tackle on Cyprus captain Constantinos Makridis but Wales clung on to their 2-1 lead to stay top of Group B.
Substitute David Cotterill and Hal Robson-Kanu had fired Wales into a two-goal lead inside 23 minutes before Vincent Laban pulled one back.
Gareth Bale, who put in another man-of-the-match performance, said: “It was a great start. We made a little mistake off a set-piece (for the Cyprus goal) but you can see how much the lads want it.”
Wales lost Simon Church with a shoulder injury in the opening minutes, and he was replaced by Cotterill, who soon made his mark.
Cotterill’s 13th minute cross evaded everyone in the box to nestle in the corner of the Cypriot net for his second Wales goal.
Bale’s brilliant back heel then allowed Robson-Kanu to run on and slot home Wales’ second .
However Laban’s free-kick found the home net via a slight touch off Wayne Hennessey’s glove to reduce the deficit.
Soon after the re-start King left his mark on the ankle of Makridis and Bale was booked for questioning the red card, but the home side managed to hang on.