La Albiceleste needed another magic moment from their talismanic skipper Lionel Messi to see off their opponents, with the seven-time Ballon d'Or winner netting a 78th-minute free kick to secure all three points.
Messi curled the ball over the wall from around 25 yards out, leaving Ecuador keeper Hernan Galindez helpless as he watched the ball sail past him into the corner.
Messi had earlier flashed an effort narrowly wide, while Lautaro Martinez also struck the post as Argentina controlled possession but found clear-cut chances difficult to create.
It took until 12 minutes from time for the Inter Miami forward to finally make the breakthrough, with his sumptuous strike taking his career tally of goals from direct free kicks up to 65.
It was also Messi's 29th goal in World Cup qualifying matches, a mark which brings him level with former Barcelona teammate and Uruguay forward Luis Suarez as the top scorer in CONMEBOL World Cup qualifying history.
Ecuador offered little threat at the other end despite matching Argentina for shots on target with three, as the world champions kept a seventh successive World Cup qualifying clean sheet at home.
Argentina's second match on the road to Canada, Mexico and the USA in 2026 comes against Bolivia on Tuesday night, while Ecuador will look to get off the mark against Uruguay that same day.
Elsewhere in qualifying, Colombia beat Venezuela 1-0 courtesy of a Rafael Borre goal, and Paraguay played out a goalless draw with Peru.
The first round of CONMEBOL World Cup qualifying fixtures will conclude tonight, when Uruguay host Chile and Brazil entertain Bolivia.
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