Gray, who didn't play in any of Jamaica's five Caribbean qualifying matches, had goals in the 13th and 42nd minutes, and Khadija Shaw added another in the 65th to move it even with Canada with three points in Group A. Canada won the opening match Wednesday, 6-0 over Panama.
Guatemala, making its debut in the CONCACAF U-17 women's finals, was on the defensive for much of the first half, not getting its first shot until Jennifer Barrios put one wide in the 51st.
Jamaica, which only scored three goals total in three games in the 2010 finals, forced Guatemala keeper Mariandre Rodas offer her line to block Gray at the edge of the area in the second minute and went ahead in the 13th.
Gray ran onto a ball from midfield and raced away from Nina Arzu before rolling a ball under Rodas and inside the right post from the fringe of the 18.
The closest Guatemala came to a scoring opportunity in the first 45 minutes came in the 38th when Jamaican keeper Chris-Ann Chambers came outside the penalty area to clear a ball from Luz Gramajo, and collided with the Chapine forward before the ball was knocked out for a corner kick.
Jamaica doubled its lead in the 42nd while playing 10-on-11.
After Oshay Nelson was treated on the field with an inhaler for an apparent asthma attack in the 41st minute, she left the field and didn't return until the start of the second half.
Regardless, Jamaica continued to push forward and Gray took a rather innocent looking ball from Broderick on the right, and unchallenged from 25 meters, turned and hit a right-footed effort that bounced twice and through the hands of Rodas, who went low to her right but couldn't come up with the ball.
Guatemala looked brighter in the second half, with Arzu getting a header wide in the 63rd in addition to Barrios' attempt.
But Shaw all but ended the Chapines' hopes, taking a ball played back to her from Gray at the edge of the center circle, dribbling within 35 meters and unleashing a right-footed drive that Rodas was able to get her fingertips to, but not divert from the upper right corner.
Guatemala next will face Panama on Friday, while Jamaica will take on Canada.