CLEVELAND (AP) -- LeBron James dropped to his knees and slapped the floor with his hand. He was exhausted and exhilarated - and one win from the NBA Finals. ''I gave everything I have,'' James said. James shook off an atrocious shooting start, withstood Atlanta's gritty comeback and battled cramps and injuries to record a triple-double, and the Cleveland Cavaliers took a 3-0 lead in the Eastern Conference finals with a 114-111 overtime victory on Sunday night. James missed his first 10 shots, but finished with 37 points, 18 rebounds and 13 assists. The Cavs needed every single one of them to hold off the top-seeded Hawks, who fought Cleveland until the final seconds despite being without injured shooter Kyle Korver and losing Al Horford, who was ejected in the first half. James, who favored his right leg for most of the fourth quarter and asked to come out of the game in OT before re-considering, hit a 3-pointer with 36.4 seconds left to put the Cavs ahead by one, and the superstar dropped a runner with 12.8 left to make it 114-111. ''He just wouldn't let us lose,'' coach David Blatt said. Atlanta had two chances to tie it in the final seconds, but Shelvin Mack missed two 3-pointers. When the final horn sounded, James collapsed to the floor and had to be helped to his feet by his teammates. It was their turn to carry him. James received treatment following the game and the four-time league MVP grimaced as he took his seat on the podium for the postgame news conference. ''I've been better,'' he said when asked how he was feeling. ''I play to exhaustion. I give as much as I can give, and sometimes the body just shuts down. ''In overtime I asked to come out, but I actually had a second thought. I wouldn't have felt right about the situation. It was mind over matter there for me. I'm playing through a lot but it doesn't matter. If I'm putting on the uniform and I'm on the floor, I have to make things happen for our team. It's that simple.'' James will have just one day to rest up before the Cavs try to earn their second Finals trip - and the fifth in a row for James - in Game 4 on Tuesday night. Jeff Teague scored 30 points and Paul Millsap 22 for the Hawks, who scratched and clawed for 53 minutes. Down 10 in the fourth, the Hawks showed championship toughness and nearly pulled off a win that would have guaranteed them another home game on Thursday. They'll have to dig deep again, and they are facing long odds to win the series as no NBA team has ever overcome a 3-0 deficit. ''I'm very proud of the way our guys competed,'' coach Mike Budenholzer said. Teague dropped a nasty, step-back jumper with 55 seconds left to put the Hawks up 111-109, but James answered - following an offensive rebound by Tristan Thompson - to knock down a corner 3 like the one he made at the buzzer to beat Chicago in the second round, making it 112-111 with 36.4 seconds left. James then hit his runner over Millsap and the Cavs and 20,000 fans held their breath as Mack took two cracks at the rim. The Cavs, who have been without forward Kevin Love since the opening round, were again missing All-Star guard Kyrie Irving, sidelined for his second straight game with an injured left knee. But Cleveland has James, and even on a night when his shot wasn't falling, he carried the Cavs, who can earn their first trip to the Finals since James took them there in 2007. Matthew Dellavedova, starting for Irving, and J.R. Smith added 17 points apiece for Cleveland. The Hawks took a one-point lead into the third quarter when James decided to seize control of the game. He recorded 15 points, six rebounds and six assists in the period as Cleveland went ahead by 10. Already in a bind, the Hawks were dealt another major blow when Horford was ejected in the final minute of the first half for throwing an elbow at Dellavedova's head. As the two hustled for a loose ball on the floor, Dellavedova rolled up on Horford's right leg and the Atlanta big man responded by bringing his right arm down hard and appearing to connect with the side of the scrappy Australian guard's face. The three officials took their time watching a review of the play before assessing Horford a Flagrant 2 and tossing him. At that point, Horford had been the Hawks' best player with 14 points. ''I did think he went at me, but I should have handled it better,'' Horford said. ''Shouldn't have gotten caught up in that and it's something I'll definitely learn from.'' A few of the Hawks accused Dellavedova of playing dirty. After all, he was the one who accidentally injured Korver in Game 2. ''I would obviously disagree with that, I was boxing him out,'' Dellavedova said. ''You can see from the baseline view that he's pulling my arm.'' James defended Dellavedova. ''We're not trying to get people hurt,'' James said. ''But you play to win the game and you play aggressively. This guy, he works his tails off every single day. He beats the odds and he comes to play as hard as he can every single night. If they're focusing on Delly, they're focusing on the wrong thing.'' NO IRVING Wearing a new knee brace, Irving was on the Quicken Loans Arena floor nearly three hours before tipoff working hard on his game. He made several quick cuts and drives to the basket, and it appeared he might be ready to give it a go after sitting out Game 2. But the Cavs announced he was sitting out 45 minutes before the game's start. TIP-INS Hawks: Atlanta shot better from the outside, but is just 21 of 79 on 3-pointers in the series. ... The Hawks went 28 of 32 from the line. Cavaliers: James has 12 postseason career triple-doubles. ... James (4,782) passed Karl Malone (4,761) for sixth place on the career scoring list. ... Since Jan. 19, the Cavs are 25-2 at home.