Tries from Tom James and Chris Czekaj were the highlights of a patchy display which saw the tourists score in either half.
Canada fought to the death thanks to tries from Sean Duke and Ed Fairhurst but they could not shrug off the kicking exploits of Biggar.
Caretaker Coach Robin McBryde took over the reigns for British Lions and Wales coach Warren Gatland and arrived in Canada without 13 of his stars on duty in South Africa. Stand-in boss McBryde's main mission will have been to see if this new-look, youthful squad could prove their worth on the highest stage before tackling southern hemisphere giants New Zealand and Australia on home soil this autumn.
Canada signalled their intent in the early exchanges by showing they were up for the fight with Pat Riordan, the Canucks captain involved in a dust-up with the Ospreys hooker Richard Hibbard after only four minutes.
Kieran Crowley's ever-improving side took the lead in the ninth minute through full-back James Pritchard's close penalty after centre Ryan Smith made an incisive midfield through the soft tackle of tackle.
Wales expected the temperatures to be soaring in Ontario but they were in danger of being caught cold as Canada looked to put the heat on Wales with some bone-crunching hits in the early stages.
The storm clouds were gathering but Pritchard held his nerve in the swirling wind to capitalise on Andrew Bishop's ill-discipline in the tackle.
But Sean Duke was caught napping following Gareth Cooper's deep kick through and slipped under pressure from centre Bishop.
Chris Czekaj pounced on the loose ball and beat Smith for the opening try to seal a sensational international return following a horror leg break in Australia two years ago.
Czekaj nearly added his second inside a minute after neat approach play by debutant Davies but Pritchard forced the Cardiff Blues wing into touch.
Canada continued to try and ruffle Wales' feathers with their physical approach but saw Luke Tait was sin-binned for killing the ball. Biggar edged Wales further ahead with two penalties for a healthy 13-6 lead before he and Pritchard swapped further kicks.
Sale Sharks scrum-half Dwayne Peel was introduced at half-time for Gareth Cooper, bound for the Cardiff Blues this summer, as Wales utilised the full range of experience within their squad.
But the visitors were rocked on their heels in the 42nd minute when flanker Robin Sowden Taylor lost possession which resulted in Duke scorching home to race under the posts.
Pritchard added the extras to tie the scores and spark wild celebrations among the passionate home supporters. But James was the catalyst with two lung-bursting runs which yielded in the second try for Wales. The first was a scintillating and mazy run to set up a chance for likewire Biggar in the right corner but the fly-half was bounced into touch just yards short of the try-line.
But Cardiff Blues young gun James was not to be denied just a minute later when he received Biggar's pass to power over for a converted try. Biggar kept up his impressive performance when his fourth penalty and sixth successful strike in total from close-range as the sun made a belated appearance. He then made it a magnificent seven in the 56th minute as Wales extended their lead to 13 points.
But Canada refused to throw the towel and scrum-half Ed Fairhurst fended off Czekaj's last-ditch tackle to cross in the right corner. Pritchard fired home the conversion to remain within one score of a global shock but Wales held on.
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