The City forward opened her account for the tournament when she headed home inside eight minutes from a searching cross to the back post.
It was the 52nd time she had found the net for the Reggae Girlz, who finished third in the previous edition of the tournament in 2018.
Host nation Mexico went close to finding an equaliser on a few occasions in a busy first half, striking the post before the 20-minute mark, while Spurs stopper Rebecca Spencer was also forced into making a fine save to deny Carolina Jaramillo.
Despite El Tri Femenil’s relative dominance leading up to the break, Jamaica were presented with a gilt edged chance to double their advantage when a VAR review spotted a handball inside the hosts’ area.
But they couldn’t take advantage, with Havana Solaun sending her penalty over the bar despite sending Mexico stopper Emily Alvarado the wrong way.
And Jamaica went even closer to a second after the break when Shaw, a constant nuisance for the host defence, struck the post.
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The City forward was played in behind by Jody Brown after she had stole possession in a dangerous area, but her chip over the onrushing Alvarado came back off the far post rather than nestling into the net.
Nonetheless, Bunny’s early header proved enough for Jamaica, who currently sit second in Group A after one match after USA’s 3-0 victory over Haiti.
And it’s a battle between the top two on Friday 8 July, as Shaw and co. look to cause an upset against the current holders in Guadalupe.
Kick-off is scheduled for 00:00 (UK), with a City-centric match report available the following morning.
