The 27-year-old forward teed up Sam Vokes for a 38th-minute opener and then scored his 23rd and 24th international goals after Joe Allen had registered his first.
Portugal's Gomes to miss Switzerland clash
Chris Coleman's Wales reached the semi-finals at the Euro 2016 before losing to eventual champions Portugal and are seeking to qualify for their first World Cup since 1958. "We had to get off to a good start in the first game," said manager Coleman. "It was going to be tough and we had to be patient and disciplined, and we were.
"We had a good level of professionalism and the supporters were great. The players got the ball and could have scored more."
Victory at the Cardiff City Stadium made Wales the early pace-setters in UEFA qualifying Group D, which also features Austria, Serbia, the Republic of Ireland and Georgia.
Rooney plays where he wants, says Allardyce
Bale is now the second-highest scorer in Wales history, four goals behind former Liverpool striker Ian Rush. "We know these games are very difficult," Bale told Sky Sports. "The teams can be difficult to break down, but we're learning to cope with that sort of play.
"We enjoyed the past, but it's history now and it's time to make some more."
Arsenal midfielder Aaron Ramsey missed Wales's Euro semi-final defeat by Portugal through suspension and he was absent again against Moldova, this time due to a hamstring injury.
On the other hand, visiting side coach Igor Dobrovolski refused to accept that the hosts were far superior on the night, and instead criticised his own players for making childish mistakes. "If Wales had been so much better, I'd congratulate them," said Dobrovolski. "But they scored four times because of our mistakes. In games like this, you can't make such childish mistakes."
Wales now face Austria in Vienna in their next game of the World Cup qualifiers on October 6.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ