Argentina, which has not lifted the Copa America since 1993, had drawn 1-1 with Chile in its opening game but secured three points thanks to Guido Rodriguez's first international goal in the 13th minute.
Messi pulled the strings for 14-time Copa runner-up La Albiceleste – beaten finalist in 2015 and 2016 – with his cross from the left flank finding Real Betis midfielder Rodriguez for his winner, which snapped Argentina's run of three consecutive draws while extending its unbeaten streak to 15 matches.
Uruguay, playing its first game of this year's tournament, was left frustrated by a resolute Argentina, while it was left to bemoan a first-half penalty appeal which was turned down.
Argentina started brightly as Messi stung the palms of Uruguay keeper Fernando Muslera with a curling seventh-minute effort, before Nicolas Otamendi had a header saved.
Messi then created space down the left for a cross which found Rodriguez, who nodded in off the inside of the post for his maiden Argentina goal.
In the 27th minute, Uruguay had a penalty shout turned down when Rodriguez appeared to make slight contact with Edinson Cavani inside the box.
Argentina raced down the other end with Messi laying off for Nahuel Molina, who tested Muslera at the near post.
Opportunities were few and far between in the second half, with Uruguay star Cavani almost glancing in a half-chance in the 69th minute while a subdued Luis Suarez flashed a volley over as Uruguay built some momentum.
Argentina struggled to create anything of note after the break, relying in attack on Messi, who was regularly crowded out by Uruguay's defence.
Argentina next returns to action against Paraguay on Tuesday (AEST), while Uruguay takes on Chile on the same day.