It took Atlanta's Jeff Teague making just one of two free throws with 1.2 seconds left and his team trailing by two points.
It took Chris Paul, who had 19 points and 10 assists, making a bank shot to give the Clippers a 109-107 lead with 54 seconds left.
It took the Clippers overcoming Blake Griffin missing two free throws with 13.4 seconds left that could have sealed the game and given Los Angeles a four-point lead.
Griffin still finished with 27 points, eight rebounds and five assists to help the Clippers win their seventh straight game.
The Clippers led by 11 points in the fourth quarter but couldn't put the Hawks away.
When Kyle Korver made a three-pointer while being fouled by Griffin and then made the free throw for a four-point play, the Clippers' lead had been sliced to 102-100 with 3:28 left.
Griffin was having a tough night handling the basketball. He had seven of the 18 Clippers turnovers.
But when the game hung in the balance, the Clippers went to Griffin down low.
He scored while being fouled, making the free throw to give the Clippers a 105-100 lead.
After Paul Millsap scored, Griffin scored again for the Clippers to push their lead back to five points.
Still, the Hawks didn't go away, pulling to within 107-105 on a three-pointer by DeMarre Carroll.
Jeff Teague tied the score at 107-107 with 1:35 left.
But Paul scored to give the Clippers a 109-107 lead that stood.
Jamal Crawford, who missed the last three games with a strained left calf, was back playing for the Clippers and back in his familiar role of sixth man.
Because of injuries to starting shooting guard J.J. Redick, who remains out with a bulging disk in his back, Crawford has started 23 games at guard for the Clippers.
But Crawford didn't play in the second half because the Clippers wanted to ease him back into action after sitting out. Crawford had his left calf wrapped up in ice. Crawford played nine minutes and 35 seconds in the first half and scored three points.
The Clippers didn't play much defense in the first quarter against the Hawks.
They allowed the Hawks to shoot 60% from the field, including 42.9% (three-for-seven) from three-point range. The Clippers gave up 32 points in the first quarter.
The Clippers played a little better defense in the second quarter, holding the Hawks to 26 points on 47.6% shooting.
But the Clippers still trailed by one point at the half.
Barnes had another big quarter to keep the Clippers close to the Hawks, scoring nine points by making all three of his three-point attempts.