Higuain collected a pass from Angel di Maria in the 11th minute and turned his marker in the box before firing a low shot past Dwayne Miller in the Jamaican goal.
The Argentines looks set for a goal-feast but despite dominating possession could not add to their tally in what was Lionel Messi's 100th appearance for his country.
Gerardo Martino's side will find out on Sunday who they meet in the next round, as will Paraguay who finished second in the group.
"The important thing was to secure qualification and we did that," Higuain said. "Now we need to rest mentally and prepare for the quarter-finals which will be very tough."
Argentina's victory meant Uruguay finished third and will face Chile in the quarter-finals in Santiago next Wednesday.
Jamaica are eliminated having lost all three of their matches 1-0. Once Higuain put them ahead, the Argentines looked certain to win comfortably.
The Napoli striker almost added a second in the 22nd minute but his lob bounced off the top of the crossbar and behind the goal.
Di Maria also rattled the crossbar before halftime and Messi came close with a rasping drive that whistled past Miller's right-hand post.
Argentina dominated the first 45 minutes in terms of possession and shots on goal but seemed to run out of ideas after the break and the match ended with the Jamaicans bombarding the Argentine goal in search of an equaliser.
Messi's 100th cap will not be remembered as one of the better matches of his glittering career. At the age of just 27, he becomes only the fifth player from his country to hit triple figures.

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