The scuffle occurred about four minutes into the third quarter. The two began to push each other as they waited for an inbounds pass under the Miami basket.
Officials reviewed the incident and then issued technical fouls and ejections to both players.
It was Ibaka's fifth career ejection, and his first this season. It was Johnson's third career ejection -- all of which have come since the beginning of last season.
"It certainly felt like there was something at stake from the very tip, and that's the way it should be in this league,'' said Heat coach Erik Spoelstra said. "There was a physicality, an edge to the game.''
Dragic brushed it off: "Nothing special. Just exchanged some words. No big deal.''
Miami held the Raptors to a season-low 89 points and halted their 12-game home winning streak, which tied the Raptors' franchise record for consecutive home wins.
Heat guard Wayne Ellington scored the go-ahead layup with less than a second remaining. Entering tonight, teams were 0-11 on potential go-ahead field goals in the final 10 seconds against the Raptors in the last three seasons.
It was the Raptors' first home loss since Nov. 5 against the Wizards. Toronto is 14-2 at home this season.
Information from The Associated Press and ESPN Stats & Information was used in this report.