Joe Allen made it 2-0 in the 44th after a poor clearance from a corner fell to the midfielder on the edge of the box and he fired past three defenders for his first international goal.
Five minutes into the second half, Bale was quick to latch onto a poor back pass by Ion Jardan and raced into the box to neatly chip past goalkeeper Ilie Cebanu before scoring his 24th Wales goal from the spot with the last kick of the match.
"We know these games are very difficult," said Bale. "We've played teams like this before who are very difficult to break down. We're learning to cope with this kind of play against us a little better, we're growing as a team.
"It was an important win for us to get off to a good start. We enjoyed the past, that's history now. It's time to make some more," he added referring to their run at the Euros in France.
The win put Wales top of the group on goal difference from Austria, who won 2-1 against hosts Georgia in the early kickoff. Ireland drew 2-2 away to Serbia in the other match in the group.
(Writing by Rex Gowar; Editing by Ken Ferris)
