Gomez curled in a shot from the right side in the 55th minute for the Americans, who avenged a loss to Jamaica last week and earned three points with Tuesday's win in front of a crowd of 24,000 at Columbus Crew Stadium.
USA, Jamaica, and Guatemala all have seven points atop Group A in the semi-final round of qualifying in North and Central America and the Caribbean (CONCACAF). The top two teams from each group advance to the final phase of qualifying next year.
Guatemala and the United States hold the edge over Jamaica with a superior goal difference. In the other group match, Guatemala defeated Antigua and Barbuda 1-0.
USA has two games left in this round as they host Antigua and Barbuda on 12 October, then travel to Guatemala four days later.
Jamaica claimed its first-ever win against the United States on Friday with a 2-1 victory in Kingston.
The United States dominated the opening half, but failed to convert their chances as the game remained scoreless going into half-time.
Jamaican goalkeeper Dwayne Miller was superb throughout. In the 20th minute, he deflected a Steve Cherundolo cross off the goal post.
American Danny Williams also had an excellent scoring chance in the 30th minute, but his shot from 25 yards out hit the post.
USA were awarded a free-kick when Clint Dempsey was fouled just outside the penalty area by Jamaica's Rodolph Austin. Gomez took the kick, placing it just inside the post as Miller got a hand on it but not enough to keep it out.
"That is my distance," Gomez said. "I feel comfortable with the ball from there. I struck it and it went in."
Mexico, meanwhile, became the first team through to the final stage of qualifying in CONCACAF after Javier Hernandez scored the only goal in a 1-0 win over Costa Rica.
El Tri started with the same line-up on Tuesday at Azteca Stadium as they had used in Friday's 2-0 away win over Costa Rica.
Manchester United striker Hernandez converted a Jorge Torres cross in the 60th minute for his 26th international goal in 41 games.
They have secured top spot in Group B with an unassailable 12 points with two games left ahead of El Salvador on five points and Costa Rica on four.