Abdulaziz Hatim opened the scoring in the 11th minute with a right-footed shot from in close that found the bottom-right corner of the goal.
Qatar dominated play, holding possession for 66 percent of the match, and it didn't take long to go up 2-0 when Akram Afif put the ball into the top-right corner on a right-footer from outside the box.
Qatar took 21 shots to Grenada's five, and led 9-2 for shots on goal. Qatar goalie Meshaal Barsham made two saves, with Jason Belton making five for Grenada.
Mohammed Muntari scored in the 36th minute on a header, and Al Moez Ali warpped things up with a goal just over a minute into the second half as Qatar moved to 1-1-0 in the tournament with four points and gets a showdown with Group D first-place Honduras (6 points) on Tuesday in Houston.