The Canadians had taken a 17-16 lead with less than 10 minutes remaining only to give away a penalty straight from the restart that allowed Laidlaw to slot the winning kick.
The hosts had the opportunity to win the match when they were awarded a kickable penalty only for referee Mike Fraser to ask for a review of an incident that floored Scotland’s replacement flyhalf Ruaridh Jackson.
Television replays showed loose forward Jebb Sinclair had hit Jackson with his elbow. He was shown a red card while the penalty was also reversed.
Laidlaw ended with 11 points, having kicked three penalties and converted lock Grant Gilchrist’s first international try.
Fullback Stuart Hogg also slotted a long-range penalty for the visitors while Canada fullback James Pritchard kicked four penalties for the home side and Jeff Hassler scored a first-half try.
Scotland now travel to Argentina for a test against the Pumas in Cordoba and finish their tour with a match against the Springboks in Port Elizabeth on June 28.
In Apia, Samoa flyhalf Tusi Pisi kicked five penalties to give his side a 15-0 win over Italy, while Fiji hammered Tonga 45-17 in their Pacific Nations Cup clash in Lautoka.
Wingers Watisoni Votu and Sireli Bobo scored two tries each in the six-try rout of the Tongans with Nemani Nadolo slotting six conversions and a penalty to go with his own try.
Japan remained unbeaten in the PNC with a composed 37-29 victory over the U.S. in Carson with fullback Ayumu Goromaru slotting 17 points from three penalties and converting all four of Japan’s tries.
Number eight Ryu Koliniasi Holani scored two tries while scrumhalf Fumiaki Tanaka and winger Akihito Yamada added the others to give the Brave Blossoms a bonus-point victory.
Eagles winger Blaine Scully helped his side to at least a bonus point in the tight game, scoring three of the team’s four tries. Number eight Cam Dolan scored the other try.
Japan lead the PNC on nine points having recorded two wins from their two games.
(Reporting by Greg Stutchbury in Wellington; Editing by Ian Ransom)