"We needed it, it's a kickstart to our campaign, hopefully it can inspire us now for the matches ahead," Bale is quoted as saying by the BBC.
Bale's first came from the penalty that he himself earned and his second was a 25-yard left-footer in the 89th minute.
"There was a bit of space in front of me, I drove into it and no one closed me down," he said, explaining his second strike. "Some go in and some don't."
Wales are now fourth in Group A with three points from three matches.