"For us, we're trying to start tuning up," Woodson said. "Every game is important. Coaches can say what they want to say but for us, I'm trying to instill if you're playing in our system you've got to play."
The Hawks (5-1) went on a 15-2 run over the end of the third quarter and start of the fourth to take a 78-62 lead.
Cook led Miami's final run with four field goals, including three 3-pointers, to pull the Heat within 89-85 with 2 minutes to play. Atlanta's Maurice Evans hit a 3-pointer to seal the win.
"Teams make runs all the time, no matter who you're playing," Woodson said. "We had an 18-point lead and got comfortable and didn't do the things that got us the lead. When that happens you either take them out and go in another direction or you tell them. `Hey, let's buckle down and start playing the game the right way."
Johnson, playing extended minutes for the first time this preseason, scored eight points in the second half. Horford pulled down 10 of his team's 26 rebounds and Marvin Williams and Maurice Evans both had 10 points.
"Our guys have grown; we've gotten better over the years," Woodson said. "I feel good about the makeup of our team."
Atlanta led 44-31 at halftime, controlling the tempo behind Horford, who had 10 points.
Wade and Udonis Haslem led a third-quarter charge that got the Heat within 63-60, before Atlanta scored the final nine points to lead by 12 heading into the fourth.
Wade scored nine points and had three assists and Haslem added 10 points in the quarter.
Wade wasn't impressed with his performance.
"Didn't hit no shots," he said.
Speolstra said he wasn't sure what his team could take out of the game.
"It wasn't played efficiently," he said. "I think both team are ready to move on to the regular season."
The Hawks used a 9-0 run to take a 23-12 lead. The Heat did little to help their cause early as they shot 19 percent from the field, including 1 of 5 on 3-pointers.
Miami's first-half futility was represented on the final play. Atlanta's Marvin Williams attempted a 3-pointer from beyond half court at the buzzer only to be fouled by the Heat's Mario Chalmers. Williams hit all three free throws as the Hawks matched their biggest lead to that point.