The Dragons found it tough to break down their stubborn opponents, eventually finding the breakthrough their efforts deserved 80 minutes in through a Hal Robson-Kanu header.
Liverpool youngster Ben Woodburn's introduction from the bench yet again proved key for the visitors, setting up the opening goal of the night soon after being brought on, before Aaron Ramsey added a second in stoppage time.
It may have been a different story had Wayne Hennessey not produced a top-class save to deny Andrei Cojocari in the 88th minute, allowing Wales to go up the other end and nick a second to move into second place in Group D.
Robson-Kanu glanced wide from a corner at one end and Artur Ionita sent a shot dipping over Hennessey's bar at the other as the two teams traded blows in a tight first half.
Cebanu was able to recover, keeping out the Arsenal midfielder's follow-up attempt before Alexandru Epureanu came to the rescue to block Robson-Kanu on the line.
That aside the Dragons struggled to create too much in an attacking sense, with Ben Davies's half-volley from 30 yards clearing the post from their only other opening.
Wales showed far more intensity to their game in the second half and came close to bagging a breakthrough goal via a Bale drive, which Cebanu got on the end of at the second attempt.
Alexandru Dedov and a lively Robson-Kanu came close for their respective sides soon after, but it remained goalless at the hour point when Chris Coleman turned to Woodburn, fresh on the back of his heroics against Austria last time out.
Despite spending much of the second half sat back in their own final third, Moldova - without a qualifying win in four years - were creating the odd opening and should have done better when Ionita got in behind but failed to pick out a teammate.
Bale was next to come close after heading wide from a corner, shortly before Ashley Williams picked out the hands of Cebanu from another set-piece delivery.
It was one-way traffic heading into the closing stages, with Ramsey curling one over and Robson-Kanu seeing a shot on the turn brilliantly blocked right in front of goal.
All the Dragons' hard work paid off 10 minutes from time thanks to Robson-Kanu's close-range header after being picked out by Woodburn down the left at the end of a positive charge.
Woodburn, who had a small penalty shout turned down with the game all square, almost marked his second appearance with a second goal when forcing Cebanu into another save.
Then came some late drama as substitute Cojocari was denied by Hennessey down low and, from the next attacking move, Ramsey sent a deflected shot over the reach of Cebanu to seal the points.
Moldova, who were heavily beaten when these sides met a year ago to the day, nearly got on the scoresheet through Dedov's shot-cross which came back off the frame of the goal, but Wales did enough to see things through.
Defeat for Ireland at home to Serbia elsewhere in Group D ensures that Wales move into second place ahead of the final batch of matches in October.