Laidlaw kicked 14 points but his greater contribution was his eye for the quick break and positive running with the ball from behind the scrum as the Scots ran in five tries against four for the Pumas.
Sibling locks Richie and Jonny Gray scored the first two tries with wingers Sean Maitland and Tommy Seymour and fullback Stuart Hogg touching down the others.
Argentina took a very early lead with a try by flanker Javier Ortega Desio but after winger Juan Imhoff was sin-binned midway through the first half they were over-run by a determined and disciplined Scotland who ran up a 24-10 halftime lead.
The Pumas, down 41-17 after the hour, had to wait until the final 11 minutes to bag another three tries, two from replacement scrumhalf Tomas Cubelli, to make the score more respectable.
Richie Gray came into the line after a Laidlaw break on the right and dummied wing Manuel Montero to score a fine opening try for Scotland that levelled the scores at 7-7 after five minutes.
Flyhalf Nicolas Sanchez, who had converted Ortega Desio鈥檚 try, put over a penalty in the 12th to restore Argentina鈥檚 lead before Imhoff鈥檚 yellow card for blocking Seymour off the ball led to a Scottish whirlwind.
Argentina, fresh from a maiden victory in the southern hemisphere Rugby championship against Australia, were second best for long spells with the Scottish players sharper and hungrier in all aspects of the game.
Jonny Gray went over from a ruck and Maitland scored in the right corner after Laidlaw broke from behind a ruck and fed him with a precise pass.
Any ideas Argentina had of a second-half comeback were quashed six minutes after the restart when Hogg dived over in the right corner with Laidlaw, who had started the move, kicking a fine conversion from the touchline.
With a number of replacements on for both teams, Argentina were awarded a penalty try in the 69th minute after a concerted attack on the Scottish line through many phases.
Juan Martin Hernandez, winning his 50th cap and having moved up to flyhalf from inside centre when Sanchez was replaced, converted and Argentina鈥檚 tails were up again.
But as the Pumas attacked from Scotland鈥檚 restart, Seymour intercepted a pass meant for replacement back Horacio Agulla and scored the home side鈥檚 fifth try.
Scotland replacement Jim Hamilton was yellow-carded eight minutes from the end and Argentine pressure brought them Cubelli鈥檚 two tries, the second a cheeky dive over a ruck.
(Reporting by Rex Gowar, editing by Ed Osmond)