Houston Rockets guard Chris Paul was also suspended for two games without pay for the fight that broke out with just over four minutes remaining in Saturday's game.
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Paul will start serving his suspension as the Rockets remain in Los Angeles to face his former team, the Los Angeles Clippers.
Ingram and Rondo will start their suspensions Monday as the Lakers host the San Antonio Spurs.
The game marked the Staples Center debut of LeBron James in a Laker uniform, but the excitement of the new era launch was overshadowed by the late-game brawl.
The Rockets were up 109-108 with 4:13 remaining when Ingram fouled Houston's James Harden. Ingram then shoved Harden and confronted referee Jason Phillips after getting a technical foul.
As that played out, Paul and Rondo got into each other's faces. The Rockets said Rondo spit at Paul. The NBA studied video of that incident Sunday.
Video replays showed that Paul appeared to push Rondo in the face, Rondo responded with two attempted punches and Paul then tried to swing back before players from both sides could separate them.
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Ingram, Paul and Rondo were all ejected. Houston won 124-115.
Paul and Rondo have been adversaries before, going back to 2009 when Paul played for New Orleans and Rondo was with Boston. They got tangled up in the second quarter of a game then, and tensions were high when the game was over - with players like Paul Pierce needing to get between the two before everyone left the court.
An NBA statement described the incident and the reason for the disciplinary measures:
Ingram has been suspended for aggressively returning to and escalating the altercation and throwing a punch in the direction of Paul, confronting a game official in a hostile manner, and instigating the overall incident by shoving Rockets guard James Harden. Rondo has been suspended for instigating a physical altercation with, and spitting and throwing multiple punches at, Paul. Paul has been suspended for poking at and making contact with the face of Rondo, and throwing multiple punches at him.
The Associated Press contributed to this report.