Chris Henry also crossed in the opening period for Ireland, but a leg injury to Sexton 16 minutes from time will concern coach Joe Schmidt ahead of next weekend's second Test at Tucuman.
That aside, though, it was a night to enjoy for the Irish.
After a lively opening 10 minutes at Resistencia, the tourists made the first impact on the scoreboard when Gabriel Ascarate was penalised for breaking the offside line, and Sexton made no mistake from the left-hand side.
From the restart Ireland were guilty of handing easy field position to their hosts when Andrew Trimble knocked on, but Greg Feek would have been thrilled to see his scrum demolish the Argentinians on their ball and the resultant penalty released the pressure.
Ireland would continue to have the upper hand at the scrum for the remainder of the first half, while a solid lineout marshalled expertly by Paul O'Connell in this 100th Test match also gave the Six Nations champions a great attacking platform.
Eight minutes after he gave his side the lead, Sexton doubled that advantage to 6-0 when the Ulster duo of Darren Cave and Like Marshall linked up well for a line-break in midfield and the scrambling Argentinian defence was forced into the concession of a penalty.
But Ireland did not have it all their own way in the first half, and after Santiagio Cordero went close to crossing in the right corner, Nicolas Sanchez got them on the board with a well-struck penalty after 27 minutes to leave it 6-3.
The Argentinian challenge was dented when No 8 Benjamin Macone was sin-binned in the 29th minute when he took Trimble out in the air, but despite their numerical inferiority, the home side stunned Ireland when Sanchez's smart break sent Manuel Montero clear to score in the corner.
Sanchez converted to give Argentina a 10-6 lead, but Ireland hit back immediately when O'Connell got the maul rolling five metres from the line and Henry dotted down.
Sexton missed the tricky conversion from the left, but Ireland would have been happy to escape the half by leading 11-10.
However, they charged into the second half with Schmidt's words echoing their ears, and three minutes after the restart Sexton rounded off a super team move to bag his side's second try.
The move stemmed from a fine lineout steal from debutant Robbie Diack, and after a powerful break from Jordi Murphy, Sexton linked up splendidly with Marshall to score an unconverted try on the right.
And just short of the hour mark, Ireland put the result beyond any doubt when Trimble intercepted Sanchez's looping pass on halfway and had the easiest of tasks to canter home unopposed for a third Irish try.
Sexton slotted the conversion but he soon limped off with a leg injury, while his replacement Ian Madigan slotted two late penalties to gloss the victory as Tomas De La Vega crossed for a late Argentinian consolation.
- Sports & Recreation
- Andrew Trimble
- Joe Schmidt