When Horford sat down with four fouls less than four minutes into the second half, Nowitzki took advantage of a matchup with Shelden Williams to score nine of the Mavericks' next 11 points.
The 6-foot-7 Johnson eventually shifted to defend the 7-foot Nowitzki, cutting off the Mavericks' momentum.
"I like taking a challenge guarding the team's best player," Johnson said. "I just wanted to stay in front of him and make him take tough shots."
Law drove past Devin Harris with 6:22 left in the first half to give Atlanta its biggest lead, 41-25. The Hawks didn't have another field goal the rest of the half as Dallas cut the lead to 46-39.
A 3-pointer by Nowitzki gave Dallas its first lead, 57-56 with 6:30 left in the third quarter, but the Hawks responded.
"They can jump, they can run with the best in the league," Nowitzki said.
Harris scored the first 10 points for Dallas but scored only one more before bruising his left thigh late in the second quarter. He did not play in the second half.
The Mavericks reported Harris' status as day-to-day.
"My thigh is pretty sore so we will see how it responds tomorrow," Harris said.
Dallas plays Sacramento on Saturday, but Harris said he hopes to play Monday against Houston.
Dallas' Josh Howard served the second game of a two-game suspension for an altercation with Sacramento center Brad Miller in a preseason game. Howard will return Saturday for a rematch with the Kings.
Forward Juwan Howard made his season debut with Dallas late in the first quarter. He joined the team Tuesday. He did not score in seven minutes. ... Mavericks owner Mark Cuban, also of "Dancing with the Stars" fame, declined an invitation to join mascot Harry the Hawk in a dance routine during a timeout. ... Pachulia began running Friday as he recovers from a sprained left knee.