Murray, seeded third in the tournament, is bidding to win his first title at Roland Garros and the Scot was rarely troubled against his world number 139 opponent, winning in one hour and 45 minutes.
A fearsome draw for Murray means he is likely to have to overcome either world number one Novak Djokovic or nine-time champion Rafael Nadal even to reach the final in Paris, but his best ever build-up on clay affords room for optimism.
There were some sloppy ground-shots, particularly on the backhand side, and he was also heard cursing his own movement early on, but apart from an unruly flock of pigeons that more than once checked his serve, there was little to make Murray feel uncomfortable.
Arguello’s preferred surface is clay but he has never made it past the first round in Paris, or any grand slam, and his ambitious attempts at winners from the back too often missed their target.
After coming through a tough opening service game, Murray broke at the first opportunity to take an early 3-0 lead but Arguello soon returned the favour, capitalising on some careless Murray ground-strokes to put the set back on serve.
Parity was short-lived, however, as a missed backhand gave Murray a second break in the eighth game and the Scot duly served out to clinch the first set.
The second set was more straightforward for the British number one, who pushed and pulled his opponent around the court with drop shots and lobs that have become a feature of his more aggressive approach in recent months.
A break in the fifth game was enough to seal the set in 39 minutes and another early in the third put the British number one on course for a comfortable victory.
“I was nervous today,” Murray said after the match.
“Always the first round of the major competitions are tough and it was quite windy, so it was tricky conditions.
“But I like being nervous, it shows you care and want to do well.
“I’m glad to have got through the first one and hopefully I can play better as the tournament goes on.”
Murray will play either Canada’s Vasek Pospisil or Portugal’s Joao Sousa in round two.