After the game, head coach Steve Bates said: "It was extremely hot out there for the lads in what was a very tough game.
"To come out here and beat England and Canada in the space of four days is absolutely fantastic."
Scotland A got into their stride in the fifth minute which Border Reivers winger Nikki Walker duly marked with the opening try. Stand-off Godman spun the ball out wide behind two decoy runners to Walker who powered through tackles from each of Canada's back three to cross the line. Fullback Calum MacRae converted.
Eight minutes later, Scotland looked to extend their lead by exploiting their strengths out wide. Glasgow Warriors centre Graeme Morrison smashed the ball up into the Canadian defence, his offload reaching MacRae who also showed terrific handling to unleash Simon Danielli who was out on the wing waiting for the final pass from Scott Gray but the ball was sent into touch by an imposing tackle on the flanker.
One of Scotland's key playmakers, Danielli continued his awesome form from Saturday's win over England in the when he received the ball in the 24th minute from MacRae. He took a blistering cross-field run and hit a midfield gap before outgunning the two Canadian centres to cross the line.
Edinburgh Gunners' Canadian fullback Mike Pyke scored for the hosts five minutes later after both wingers were utilised on the right flank where Pyke hit the ball at pace. James Pritchard converted.
Canada sevens player Justin Mensah-Coker came out of his shell in the second half to really menace the Scots as Danielli had done in the first half.
The winger came close to putting the home side ahead after 47 minutes when the Canadians broke the Scotland line in mid-field. Mensah-Coker darted up the left but was brought down short.
Mensah-Coker again proved difficult for Scotland in the 56th minute when Danielli tried to squeeze into the right corner only for the sevens star to shove him into touch.
Again proving a handful for the Scotland defence, Mensah-Coker chipped through from beyond the half way line and continued his skills with the boot up the left wing. His final attempt to set chip the ball into the scoring zone however was a little too heavy and went dead before he could touch down.
In the dying minutes, Scotland's forwards pounded the Canadian defence on the home 22 meter line. The forwards' efforts set up a solid platform for Godman to receive the ball in the pocket and slot a drop goal to put the Scots five points ahead.
Canadian kicker Pritchard took a gutsy decision in the final minutes of the game to pull Canada closer to Scotland but missed the vital opportunity.