The Heat matched the fourth-longest single-season win streak in league history, trailing only the 20 in a row by Milwaukee in 1970/71, Houston's 22 in a row in 2007/08 and the Los Angeles Lakers' record run of 33 from 1971/72.
Miami also matched the record for the longest win streak by a defending NBA champions, a 19-game run by Boston in the 2008/09 campaign.
"Ten is enough for me," Chris Bosh, the third pillar of this Heat line-up, said. "Twenty's cool. I'd take it."
Wade contributed six assists and five steals while James added seven assists and seven rebounds on a night when he made only 3-of-11 shots from the field as the Heat won a 15th home game in a row, improving to 30-3 at home this season.
"Leading with our defense has been the key for us," Wade said. "We come out defensive minded from the beginning of the game."
The Heat, 48-14, have not dropped a home game since losing to Chicago on January 4. But Miami will embark upon a five-game road trip that starts on Wednesday at Philadelphia and includes stops in Milwaukee, Toronto, Boston and Cleveland.
Wade said the Miami bench is a major factor in sustaining the win streak.
"The key is our depth," Wade said. "We come in waves. Our bench has definitely got to come to play."
The Heat scored 27 points off a season-high 24 Atlanta turnovers and never trailed in producing the 14th double-digit victory margin in the team's record run.
Miami, the only NBA team to clinch a play-off spot and also the only team to have beaten every other NBA team this season, led the Hawks by as many as 22 points.
Josh Smith led Atlanta with 15 points but the Hawks, 34-29, have dropped eight consecutive meetings with the Heat.
"Let's be honest, guys," James said in the locker room after the game.
"We're not sitting here and saying this is not something special. This is an unbelievable streak that we're on. We're playing great basketball. We're winning in different phases of the game, we're playing different styles, we've won every game, on the road, at home, double-overtime games, end-of-regulation games, whatever the case may be."
Follow us @SprtNationalUAE