The incident which turned an otherwise entertaining contest into somewhat of a sluggish affair happened four minutes from half-time when Georgian flanker Viktor Kolelishvili landed a dangerous tackle on Canada fly-half Liam Underwood which resulted in a multi-player punch-up.
Kolelishvili and Canada captain Tyler Ardron subsequently played no further part in the match.
Georgian full-back Merab Kvirikashvili kicked 14 points with winger Tedore Zibzibadze the only man to score a try.
Canada's points came from penalties by Underwood and Harry Jones.
Jones was forced to take over the kicking duties after Underwood had retired hurt and through his boot Canada enjoyed a 12-9 lead at half-time.
Then came Zibzibadze's moment of brilliance was followed-up by a well executed conversion from out wide which handed the lead back to Georgia in the 51st minute.
Kvirikashvili converted another penalty at the 61-minute mark in what turned out to be the final score of the contest.
Canada take on Romania in Bucharest next week.
Man of the match: Merab Kvirikashvili's kicking proved to be vital in this slugfest.
Moment of the match: It has to be Tendore Zizibadze's try.
Villains of the match: All the players who were involved in the punch-up. With special mention to Tyler Ardron and Victor Kolelishvili who saw red for their actions.
Try: Tendore Zizibadze
Con: Merab Kvirikashvili
Pens: Kvirikashvili 4
Red card: Kolelishvili
Pens: Underwood 3, Jones 2
Red card: Ardron