Allen hit his second 3 of the game with 1:48 left in the first quarter to reach 2,561 in his career - a number that flashed on the scoreboard in green and white while the TD Garden erupted in applause.
The 38-year-old Celtic celebrated little as he got back on defense, but at the next whistle went over to Miller for a hug and a handshake, then bumped fists with Lakers star Kobe Bryant.
"I'm just so happy for him because this is one of the best guys," Miller said on the TNT broadcast. "He's so humble, he's so giving, he's a great family man and I'm excited. This is great. This is great for the game of basketball. You know why? We're focusing and talking about shooting."
The record-breaker came on a transition basket from the right side on a pass from Rajon Rondo. The sold-out crowd at the TD Garden - the visit by the rival Lakers would have been enough for that - cheered, and his teammates rose out of their seats.
After the quarter ended, Allen exchanged a few words and another hug with Miller, then went down the sideline to receive his family's congratulations.
"It's so serendipitous that it happened the way it happened. For us to be sitting here, Reggie's in the building and he's in the building able to work the game," Allen said before the game. "He just told me he was proud of me and he was excited for me. He said he was glad that he could be here in this moment."
Miller has been cheering Allen on as he pursed the record, and the former Indiana Pacers star said people shouldn't be surprised.
"All records are made to be broken," Miller said. "I had a conversation with Ray earlier tonight and he was like, 'When I was a rookie and I came to Market Square Arena and I saw you for 3 to 3½ hours before (the game) shooting, that's how I wanted to patent my game."'
A 6-foot-5 guard from Connecticut, Allen is the No. 25 scorer in NBA history, entering the night with 21,855 points in a 15 year career with Milwaukee, Seattle and Boston. He is already the NBA's all-time leader in 3-pointers made per game since the shot was introduced to the league in 1979, with an average of 2.4.
"He's just a machine," Celtics coach Doc Rivers said before the game. "He shoots every day. He works on it. He runs every day. You look at his body. If you're a young player just look at Ray Allen if you want a long career. He's the ultimate pro."
Allen got to the record a little faster than Miller, needing 6,430 shots to reach the record - a percentage of 39.8. Miller took 6,486 shots from 3-point range in his 18-year career with the Indiana Pacers, making 39.5 percent.
Allen said beforehand he had unexpected trouble sleeping on Wednesday night, with the combined anticipation of an NBA finals rematch against the archrival Lakers and the chance to break the record.
"I was like a little kid," he said. "Just the game itself is big enough and being on the precipice of breaking this record takes you to another level. ... Being here in this moment and being able to say this moment is before us, it seems pretty overwhelming."
Allen entered the season needing 117 to pass Miller, and he entered the night needing one to tie and two for the record. With the crowd cheering in anticipation every time he got the ball beyond the arc, he missed his first attempt and then made his second, from the top of the key.
Allen gave a fist pump while teammate Nate Robinson raised one finger in the air. The next time down, Paul Pierce passed him the ball on the left side and Allen fired up another shot that, to the crowd's dismay, went off the rim. He missed the next try, too, but then got the record on his fifth 3-point attempt of the game.
"I think it's a remarkable thing he's achieving tonight," Lakers coach Phil Jackson said before the game. "It is something to watch for and I hope he gets rid of it right away."
During the second quarter, the Celtics showed a video with him making 3-pointers through his career - first with the Milwaukee Bucks and then with the Seattle SuperSonics. The number "2,561" was repeated in green and white on the message board that ringed the scoreboard and on the one that circled the arena.