Guyana now leads Group B with 10 points from four games. Trinidad and Tobago is next with nine points. The rivals play each other twice next month.
John Barry Nusum scored for Bermuda in the 72nd minute, powering a header past goalkeeper Ronson Williams.
But Shakes was left alone at the far post and headed the ball past Freddie Hall.
Bermuda had a chance to go in front late in the game, but Nusum and Nahki Wells both shot straight at Williams in the final minute.