Torrential rain, thunder and lightning could not halt a compelling contest which saw Ireland 'A' full-back Denis Hurley and centre Fergus McFadden cross for early tries, referee Matthew Goddard also awarded a penalty try and replacement hooker Denis Fogarty settled the issue late on with a fourth touchdown.
Canada led 16-13 at half-time after Ander Monro kicked two penalties and a drop goal and also added the conversion to Phil Mack's well-taken try.
Out-half Niall O'Connor pulled Ireland 'A' back and although Monro kicked Canada ahead 19-16, the Irish pulled away with a workmanlike display in the final quarter.
Speaking afterwards, man-of-the-match Toner said: "It was my first cap for Ireland 'A' so I'm pretty happy. We have been together a week now and that showed at the end when things came off.
"Canada were very much up for it but we had a point to prove as it was our first game together as an 'A' team.
"We gave away a lot of penalties and their kicker (Monro) was on form but we improved and are happy overall, especially given the conditions."
Livewire scrum half Isaac Boss, who captained the Irish on the day, said: "We were a little bit rusty at the start but we pulled out a win. Credit to Canada, they made it tough for us and are a quality international side.
"Now we are looking forward to the next game against Georgia and trying to qualify for the final."
Ireland 'A', coached for this tournament by Declan Kidney and Ireland's Grand Slam-winning management team, will play the Georgians at Infinity Park in Glendale, Colorado on Sunday (kick-off 3.30pm local time/10/30pm Irish time).