Korver's 3 with 5:29 remaining in the first quarter broke a tie with Dana Barros (1994-96).
"It feels good, I'm glad it's done" Korver said after scoring 10 points and making 2 of 3 from beyond the arc. "My naps the last couple (game days) haven't been very solid. I'm the product of good team basketball, of setting screens and (getting) good passes and floor spacing and all of that.
"There's a lot of thanks to go around ... players who aren't here, coaches who aren't here this year and this group in here. I just said, `Thank you.'"
Korver has made 47 percent of his 3-point shots (235 of 502) during the streak.
Hawks coach Mike Budenholzer said he didn't think the team went out of its way to get the 11-year veteran from Creighton the ball in position to break the record, but admitted that his players might say otherwise.
Korver missed his first try just 1:03 into the game as fans rose from their seats as he rose to shoot. Everybody in Philips Arena stood up again just an instant before the record-setter swished to give Atlanta an 18-10 lead.
"DeMarre (Carroll) passed up a wide-open shot to try to get him the ball, and I gave up a transition try," said Atlanta point guard Jeff Teague, who scored 13 points. "I wish I made the pass."
That honor went to forward Paul Millsap, who scored 16 points and tied his season high with 14 rebounds to help offset a season-high 30 points off the bench by Cleveland's Dion Waiters.
Millsap, who was also a teammate of Korver's with the Jazz, was more proud of his assist to Korver than anything else.
"I'm in the history book now," he said with a smile. "I'm in awe to see something like that. Teams focus on keeping him off the 3-point line, and for him to do that for so long is an amazing accomplishment."
Atlanta (11-10) won with balance as seven Hawks scored in double figures and the home team had little trouble with the Cavs (6-13), who fell to 1-10 on the road.
Jarrett Jack added 13 points off the bench for Cleveland, but all Cavs other than him, Waiters and Bynum (20 points, season-high 13 rebounds) combined to shoot 12 for 50.
Cleveland starters Kyrie Irving and Alonzo Gee went scoreless. Irving, who entered the game averaging 20.8 points per game, shot 0 for 9.
Atlanta raced to a 37-20 lead in the first quarter while Korver made two of Atlanta's five 3s in the period. Millsap connected from 50 feet as the buzzer sounded.
Atlanta did not make a 3 in the second quarter, yet built a 63-43 halftime lead as Millsap had 14 points and seven rebounds in the first two periods.
Cleveland went on a 12-0 run in the third quarter, pulling to 77-60 on Bynum's putback.
Waiters and rookie guard Matthew Dellavedova hit 3-pointers on consecutive possessions to pull the Cavs to 84-72 early in the fourth before Atlanta steadily pulled away.
Waiters shot 13 for 20 shots, but lamented the Cavs' slow start and lethargic showing.
"We've got to come out with a sense of urgency," he said. "It's frustrating to have to keep talking about the same thing over and over.
"Superman's not coming in the locker room to help us. It's just us. We're all we've got so at the end of the day we've got to come out and play, play the right way, too."
Cleveland entered the night having won back-to-back games for the first time this season, but was never really in this game. The Cavs trailed 77-48 in the third quarter.
"We've got to come out, we've got to compete for 48 minutes," Cleveland coach Mike Brown said. "We've got to find a grittiness ... I'm not worried about Kyrie's shot. He's going to make enough shots."
Hawks reserve post man Gustavo Ayon suffered a left ankle sprain and a left leg contusion in the final minute of the game. His status for Tuesday's game against the Thunder was not announced.
Copyright by STATS LLC and The Associated Press
ATLANTA, GA - DECEMBER 06: A general view of Philips Arena next to the CNN Center in downtown Atlanta prior to...