David Cotterill broke the deadlock in the 13th minute for the home side having come on as an early substitute for the injured Simon Church at the Cardiff City Stadium.
Hal Robson-Kanu showed great composure in converting the second 10 minutes later, but Vincent Laban halved the deficit from a set-piece nine minutes before the break.
Having looked full of confidence at 2-0 up, Wales were given more cause for concern at the beginning of the second half when Andy King was sent off for a reckless challenge on Konstantinos Makridis.
But Chris Coleman's men clung on to to make it seven points from a possible nine in Group B so far to remain top.
Coleman made two changes to the side that drew 0-0 with Bosnia-Herzegovina on Friday, with Robson-Kanu and George Williams coming in for Ben Davies and the injured Jonathan Williams, but a shoulder injury to Church prompted Cotterill's introduction in the sixth minute.
Gareth Bale tested Tassos Kissas with an early free-kick from 25 yards after being cynically felled by Marios Nikolaou, and routinely tried his luck from distance.
George Williams – making his full debut - showed good pace as he darted into the penalty area to force a corner, which eventually led to the home side's somewhat fortuitous 13th-minute opener.
The initial set-piece was cleared but the loose ball fell to Cotterill, who sent a cross into the box that evaded everybody, including Kissas who was in no-man's land.
Cotterill's second international goal appeared to give Wales added confidence and, after Cyprus had tried their luck through Pieros Sotiriou, Robson-Kanu capped an incisive attack to double the advantage.
A move that started at the heart of the Welsh defence ended with Robson-Kanu getting on the end of a neat Bale flick to coolly slot past Kissas.
However, a degree of complacency crept into Wales' play and they were punished when Wayne Hennessey – excellent on Friday – carelessly rushed off his line to punch a Laban free-kick, but failed to make a strong enough contact with the ball.
Bale saw a deflected free-kick tipped onto the crossbar just before the interval and Joe Ledley's header from the rebound was cleared off the line by Giorgios Merkis.
Just as they had in the first, Wales started the second half by losing a man.
This time it was a red card for King, who mis-timed a challenge on Makridis, raking his studs on the midfielder's Achilles to earn his marching orders.
The sending off disrupted the pace of the match, with chances few and far between for both sides thereafter, although Bale sent the ball crawling along the goalline from a tight angle on 70 minutes.
With Cyprus having dominated possession for much of the second half, Giorgos Efrem headed narrowly over five minutes from the end, but Wales did enough to hold on and remain one point clear at the top of the group.
