The Hawks won in the coaching debut of Larry Drew, who replaced Mike Woodson after Atlanta was swept out of the playoffs by Orlando in the Eastern Conference semifinals.
Atlanta scored 12 straight points late in the third period and took a 16-point lead into the final quarter. Memphis came no closer than 11 points over the last 12 minutes.
Johnson scored 22 points, and Zaza Pachulia added 17 and 11 rebounds off the bench.
Mike Conley paced the Grizzlies with 23 points. Memphis lost its opening game of the season for the 10th straight year and did so after going unbeaten in its seven exhibition contests.