The Napoli forward made his first start of the tournament in Saturday's match, and coach Gerardo Martino – who was watching from the stands after being sent off in the clash with Uruguay – would have been pleased to see the change work to great effect.
Argentina were looking to celebrate Lionel Messi's 100th cap for Argentina in fine style, and they dominated from the outset.
After a period of pressure Higuain grabbed the opener with a smart finish. Angel Di Maria was fed the ball on the left, with the Manchester United midfielder moving inside to the edge of the penalty area before squaring the ball to Higuain who held off a defender and turned well as put the ball past Jamaican keeper Dwayne Miller.
Higuain nearly made it two in the 22nd, lopping the ball over Miller after being put through on goal by Lucas Biglia, but his effort came back off the crossbar.
Argentina had multiple chances to increase their advantage, but Jamaica somehow stood firm and restricted the damage to 1-0 at the break.
The crossbar once again came to the Caribbean side's rescue, with Di Maria finding the woodwork with an effort from the edge of the area that had Miller beaten.
Jamaica finished the match strongly, and while they insured that no further damage was inflicted, they could not find their first goal of the tournament.
The win sees Argentina finish ahead of Paraguay and Uruguay who drew earlier in the day. A clash with either Venezuela or Ecuador awaits Martino's side.