The Euro 2016 semi-finalists initially faced spirited Moldovan resistance but led 2-0 at half-time thanks to goals from Sam Vokes and Joe Allen.
Gareth Bale seized on a woeful pass for the third, then netted a last-minute penalty for his second of the night.
Wales' win puts them top of Group D on goal difference ahead of Austria.
Chris Coleman's men travel to Vienna for their next World Cup qualifier on Thursday, 6 October.
As the group's top seeds, Coleman's side had been expected to make light work of Moldova, who are ranked 154 places below them in the world rankings.
After a cagey first half hour they eventually did so with a flourish, becoming the first team to score three or more goals against the eastern European minnows since England's 4-0 victory in 2013.
