Harris backed up his claim by making 7 of 8 shots from the field. He added five assists.
"Devin knocked down some shots, but I thought the way he pushed the basketball, that was the difference," Drew said. "That's the Devin Harris of old."
Atlanta had not lost more than two straight games before hitting the four-game skid.
Drew said he reminded his players other successful teams had similar or worse losing streaks this season.
"You don't hang your heads and feel sorry for yourself because you lost four in a row," Drew said.
Utah took its biggest lead late in the third period when a 3-pointer by Hawks rookie John Jenkins sparked an 8-1 run as Atlanta cut the lead to 76-68 entering the final period.
Pachulia opened the fourth period with back-to-back baskets as the Hawks cut the deficit to four points.
Harris hit a 3-pointer to cut Utah's lead to 82-79 and made only 1 of 3 free throws 40 seconds later to trim the deficit to two points.
The Hawks finally pulled even at 85-all with 5:48 remaining when Harris had a steal to set up his 3-pointer.
Jazz forward Marvin Williams, traded to Utah in the offseason following seven seasons with the Hawks, was with the team but not in uniform in his first return to Atlanta. Williams, who was held out with inflammation in his right knee, visited his former Hawks teammates before the game.
Harris was acquired by Atlanta in the Williams trade, but he insisted it didn't matter that his big game came against his former team.
Drew started Harris with Jeff Teague in the backcourt and Kyle Korver at small forward as he tweaked the lineup.
NOTES: Former Hawks star Dominique Wilkins, on press row as a TV color analyst, was presented a birthday cake during a break. Wilkins celebrates his 53rd birthday on Saturday. ... Korver hit a 3-pointer in the first quarter to give him 3s in a personal-best 29 consecutive games. It is tied with Mookie Blaylock for the second-longest streak in Hawks history. ... Foye had 15 points in the first quarter as he made each of his three 3-pointers.