The Napoli striker was on target after 11 minutes in a game that saw the South American side dominate but fail to add to their slender lead throughout a one-sided affair in Vina del Mar, Chile.
Despite boasting a host of stellar attacking options, questions hung over coach Gerardo Martino's ability to maximise his side's goalscoring potential after netting just three times in the first two games.
Consequently, Martino made a bold move prior to kickoff by dropping Sergio Aguero - who scored 32 goals for Manchester City in all competitions last season - in favour of Higuain following the Albiceleste's underwhelming start to the competition.
The switch was nearly swiftly justified when Higuain found himself with a number of chances early on, before opening the scoring on 11 minutes.
Angel di Maria was the architect as the Manchester United winger galloped down the flank before cutting back for the former Real Madrid marksman, who swiveled his marker and found the bottom corner in style.
After beating Uruguay 1-0, Martino admitted that he was worried by his side's lack of killer instinct - concerns that would have re-surfaced when Lucas Biglia volleyed narrowly wide, before Higuain's clever dink bounced off the crossbar on 23 minutes.
There was further frustration when Lionel Messi - on the night of his 100th cap - curled just wide of the far post, with Di Maria then watching his effort get cleared off the line as Argentina were made to settle for a 1-0 half-time lead.
The woodwork came to Jamaica's rescue once more on 52 minutes as Martino's men picked up where they left off, with Di Maria's strike cannoning off the crossbar.
Higuain was culpable for yet another miss on the hour mark, while Lance Laing stood over a free kick at the other end in a rare moment of optimism for Jamaica, but his effort ended up sailing well over the bar to sum up their night.