With Dallas' interior defense and rebounding gutted by the loss of Chandler, Jordan dominated while Chris Paul led the Clippers with 25 points and 13 assists.
Chandler injured his left ankle just 39 seconds in and went to the locker room about a minute later. Ellis joined him there with 8:03 left in the first quarter after hurting his left hip.
The Dallas injuries came on a night that started with news that Griffin would be out three to four weeks after surgery earlier in the day for a staph infection in his right elbow.
Charlie Villanueva tried to keep Dallas in the game by scoring 13 points in the last 5 minutes of the first quarter and finished with a season-high 26.
But the Mavericks, already missing point guard Rajon Rondo with an orbital bone fracture, just couldn't keep up without their leading scorer in Ellis and primary rim protector in Chandler.
Chandler was injured when he was fouled by Spencer Hawes on a layup attempt. He made the first free throw but missed the second and had to stay in the game until the next whistle about a minute later. He was replaced by Greg Smith.
It wasn't clear when Ellis got hurt.
The best illustration of the struggle without Chandler came early in the fourth quarter, when guard Devin Harris tried to keep Jordan from scoring by grabbing him and throwing him to the ground as the shot went in. Jordan, who also had three blocks, missed the free throw, but the Clippers still had their biggest lead to that point at 98-80.
Dirk Nowitzki scored 18 points for Dallas, while Chandler Parsons had 16 points and a season-high 12 rebounds.
Before the Mavericks were scrambling to replace Chandler and Ellis, the talk was about how the Clippers could hang on to their playoff spot in the difficult Western Conference without Griffin, the All-Star forward who was replaced for Sunday's game by Portland guard Damian Lillard.
Coach Doc Rivers was at least somewhat relieved that the timetable on Griffin was what he expected, and that one of those weeks will be the All-Star break.
"I feel very good about our team," Rivers said before the game. "Obviously, we've lost some games. We have injuries and all that. You go through stuff. The panic is outside the locker room. It's not inside the locker room."
Rivers said the contributions will have to come from everywhere, and there were other contributors a night after the Clippers were blown out in Oklahoma City in their first game without Griffin.
Jamal Crawford scored 18, while J.J. Redick was 3 of 4 from 3-point range and had 15 points after missing three games with back spasms. Matt Barnes had 12 points and seven rebounds, and Paul added six rebounds.
Clippers: Jordan's 27 rebounds were the most against the Mavericks since Dennis Rodman had that many for Chicago on Dec. 29, 1997. ... Glen Davis returned after leaving the Oklahoma City game with back spasms. He played three minutes.
Mavericks: Villanueva's point total was his highest since scoring 30 for Detroit against the Clippers on Nov. 12, 2010. ... J.J. Barea, starting in Rondo's spot again, had 15 points and seven assists.
Clippers: Host Houston on Wednesday night.
Mavericks: Host Utah on Wednesday night.