Johnson, subbing for the injured Al Hoford, drained the game-winning free throw with 4.6 seconds remaining to cap his run as the Hawks bounced back from an 18-point, second-half deficit.
Atlanta continued its mastery over Minnesota, downing the Timberwolves for the 11th straight time.
Kevin Love pumped in 30 points and grabbed 13 boards for Minnesota.
Spanish rookie Ricky Rubio contributed 18 points and 12 assists.
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