The U.S, who suffered a 2-1 defeat to the Jamaicans in Kingston on Friday, are now tied on seven points at the top of group A with Guatemala and Jamaica with two games remaining in the phase.
With only the top two from the group progressing to the final round of qualifying, the U.S still have plenty of work to do in October's games away to Antigua and Barbuda and at home to Guatemala.
But their task would have been much tougher had they not taken the maximum points from Tuesday's game.
U.S coach Jurgen Klinsmann made five changes from Friday's defeated line-up and brought in some much-needed width with Graham Zusi on the right and Jose Torres on the left while Danny Williams was given the main defensive midfield responsibility.
The switch worked well with the U.S. dominating possession heavily in the opening 45 minutes and only the woodwork and great keeping from Dwayne Miller leaving the visitors on level terms.
Zusi made an instant impact hitting the bar with a shot from the edge of the area in the sixth minute and then 14 minutes later Steve Cherundolo saw his low shot deflected, forcing a great save from Miller who tipped the ball against the post.
Miller was again down close to foil Zusi at the back post as the U.S camped inside Jamaica's half but he was just a bystander as a thundering strike from Williams crashed against the post.
The breakthrough finally came 10 minutes after the interval when Gomez curled a free-kick inside Miller's left-hand post and while the keeper should have done better, few could argue that the Americans deserved their lead.
With the advantage in place and the Caribbean side showing more attacking intent as they searched for an equaliser, the U.S struggled to create more chances but it was a night that was all about picking up three crucial points on the road to Rio.
"It was important for us to regroup after what happened in Jamaica, we knew it wasn't our best performance," said Gomez.
"It wasn't always pretty but I think we did the job well," added the striker.
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