But instead of crumbling, the Clippers rose to the challenge as Chris Paul got hot and helped Los Angeles erase the deficit by halftime and hold on for the 118-107 win.
Paul had 30 points and 12 assists and Jamal Crawford added 22 points to help the Clippers clinch their franchise-record third straight playoff appearance.
Coach Doc Rivers was pleased at how his team responded to the adversity.
"We're here to win games and our guys are growing up, they're mature and it was great," Rivers said.
That's something that Matt Barnes believes was lacking from the team a year ago.
"We knew last year that was our weakness, that we were mentally weak and I think that we put a collective focus on being mentally tough and we've (come) a long way this year," he said.
"You can't use that as an excuse," Houston's Chandler Parsons. "Everybody goes through injuries. They didn't have their best player, either ... We have to learn to win games without guys and hope they can get back as soon as possible."
The Clippers trailed by as many as 15 points in the first half before using two big runs to take the lead. Houston stuck around for most of the second half before consecutive 3s by Barnes and Darren Collison made it 114-101 late in the fourth.
Griffin, whom Rivers said is day to day, didn't return after leaving in the first quarter and Davis missed the second half for disciplinary reasons because of his second-quarter incident.
James Harden led the Rockets with 32 points, and Chandler Parsons had 28. DeAndre Jordan added 20 points, 12 rebounds and six blocks for the Clippers, who swept Houston this season and are third in the Western Conference.
Jordan and the Clippers didn't make a big deal out of securing a playoff berth.
"It's another goal that's accomplished," he said. "It's definitely not the only thing we want to accomplish this season, but it's a start. Now we've just got to keep building and win as many games as possible and hit our stride when they playoffs start."
Crawford scored all of the Clippers' points in an 8-1 run to start the fourth quarter and leave them up 96-85. An 8-3 run by Houston cut the lead to 102-96 with five minutes remaining. Harden capped it with a free throw after a technical foul on Paul.
The Rockets scored the first five points of the third quarter to take a 63-61 lead. The teams exchanged the lead several times in that quarter before a layup by Ryan Hollins left Los Angeles up 88-84 entering the fourth quarter.
The first half was filled with drama for the Clippers, who lost Griffin in the first quarter before the incident with Davis in the second.
There appeared to be minimal contact between Griffin and Donatas Motiejunas before Griffin dropped to his hands and knees on his way to the bench after a timeout was called midway through the first quarter.
He was clutching his lower back and remained on the court for a couple of minutes before being helped to his feet. He was biting his jersey as he gingerly walked off the court and to the locker room.
Davis, whose nickname is "Big Baby," was apparently upset after being taken out in the second quarter and threw a temper tantrum at Rivers, who immediately sent him to the locker room. The team announced that he would not return after halftime.
Davis was 0-for-2 with a steal in less than four minutes in the first half.
"I thought Baby was just too emotional and for me if you're too emotional I just always send you back to the locker room and keep you back there until the next game," Rivers said. "But I love Baby. I just didn't think emotionally he was ready to play tonight."
With Griffin out, Houston used a 7-2 spurt to start the second quarter and extend its advantage to 40-25.
The Rockets were still up by 15 points a couple of minutes later when the Clippers used an 8-0 run to cut the lead to 44-37. Harden made three free throws before another run -- this one 14-2 -- gave Los Angeles a 51-49 lead.
Los Angeles led by a point soon after that before scoring six straight points to extend the lead to 61-54. Houston scored the last four points of the quarter to cut the lead to 61-58 at halftime.
Jordan went to high school in Houston and college at nearby Texas A&M. ... Howard is day to day with a left ankle strain and Beverley has a torn meniscus in his right knee and is out indefinitely.