Johnson was picked by commissioner David Stern to replace Jason Kidd, who has a back injury. Johnson, who got the news on the team bus heading to Wednesday morning's shootaround, is Atlanta's first All-Star since Shareef Abdur-Rahim in 2002.
"It's my first All-Star game, so I'm definitely going to be excited and anxious to get out there and play," Johnson said.
The Hawks trailed 75-62 heading into the fourth quarter, but Johnson's short running jumper gave them a 92-90 lead with 19 seconds remaining, and he was 4-of-4 from the line afterward to keep them ahead.
"I thought we focused in the fourth quarter," he said. "Throughout this whole year, we have been bogged down with injuries and haven't had just one fit lineup.
"So it's been tough on us with our chemistry part, but we have started to come together later in the season."
Josh Smith added 19 points and had 11 rebounds for Atlanta. Reserve Zaza Pachulia had 15 points and 12 rebounds for the Hawks, who have won six of their last seven road games.
Cuttino Mobley had a season-high 31 points for the Clippers, but strained his left groin and failed to score on the only two shots he took in the fourth quarter.
Chris Kaman had 20 points, 13 rebounds and blocked six shots for Los Angeles, but missed two critical shots in the waning seconds and had another blocked by Smith after Atlanta took the lead for good.
"We just let them back into the game," Kaman said. "It happens all the time, and after a while, you just ask yourself what you are going to do. We can't finish a game in our own building against a team that we are supposed to beat."
The Clippers again were without Elton Brand, their leading scorer (20.7) and rebounder (9.2). He sat out his second consecutive game because of back spasms. The two-time All-Star forward now will have time to recover, since the All-Star Break is this weekend and the Clippers don't play again until next Tuesday.
"This was a horrible loss for us," Clippers coach Mike Dunleavy said. "We had a 13-point lead in the fourth quarter. We got beat too easily off the dribble. Some of our guys need to take these (All-Star Break days) off and get their heads straight defensively."
Atlanta swept the season series 2-0 after the Clippers took both meetings in each of the three previous seasons.
Mobley, who missed just one of his nine shots from the floor in the first half, finished 12-of-18. He made all six of his shots -- including four 3-pointers -- and scored 16 of his 20 first-half points in the second quarter to help Los Angeles bounce back from a 26-19 deficit early in the period.
They led 45-43 at halftime.
Johnson had 12 points to top the Hawks' scoring in the first half.
Atlanta led 24-19 at the end of the first quarter, going 9-of-19 from the floor to the Clippers' 6-of-18. Los Angeles found the range in the second quarter, going 10-of-17 to the Hawks' 9-of-20.
Since it was Valentine's Day, the Clippers chose to wear red road jerseys and Atlanta wore white. The Clippers are 8-19 on the road this season. ... Dunleavy said before the game that he wasn't considering playing Brand, even if he offered. "It would be too risky," the Clippers coach said. "Besides, with the All-Star Break coming up, it just makes sense to get him right."