Now the Celtics must try to keep winning without their leader, who suffered a torn anterior cruciate ligament in his right knee late in Friday's 123-112 win, also in double overtime, in Atlanta.
They won Sunday after Pierce's 22-foot jumper with 31 seconds left gave them a 99-98 lead.
But making the playoffs got harder as the Celtics try to hang on to the eighth and final postseason spot in the conference.
"Obviously, the Rondo news is pretty tough. I knew it before the game," Rivers said. "I just didn't think it was any time to tell any of our guys."
The game was the first in Boston for Ray Allen since he left the Celtics after five seasons and signed as a free agent with Miami. He scored 21 points.
Kevin Garnett had 24 points and 11 rebounds, and Pierce added 17 points, 13 rebounds and 10 assists for the Celtics.
Rondo's injury "puts this team and the rest of the guys in a position to be ready to step up," Pierce said. Sunday's win "was a perfect example. We showed we are capable."
James had 34 points for the Heat, whose winning streak stopped at four.
"As much as I've been a rival with Boston over the years, I never want to see anyone go down," James said. "It's terrible, not only for their team but for the league."
In other games *
At Los Angeles, Kobe Bryant had 21 points, 14 assists and nine rebounds, Steve Nash added seven of his 17 points in the final 5 1/2 minutes, and the Lakers held off the NBA-leading Oklahoma City Thunder, 105-96.
Kevin Durant scored 35 points and Russell Westbrook had 17 points, 13 assists and nine rebounds for the road-weary Thunder, who finished their longest trip of the season at 3-3.
* At New York, Carmelo Anthony tied a franchise record with nine three-pointers, then converted a go-ahead, three-point play with 12.5 seconds left to cap a 42-point night and lead the Knicks to a 106-104 victory over the Atlanta Hawks.
The Hawks shot a season-high 60 percent from the field but had their three-game winning streak snapped when Josh Smith, burned on Anthony's basket, missed a three-pointer on Atlanta's final possession.
* At Dallas, Shawn Marion scored 18 points in his 1,000th game, Dirk Nowitzki also had 18 while passing Allen Iverson on the career scoring list and the Mavericks beat the Phoenix Suns, 110-95.
Nowitzki passed Iverson for 18th on the NBA's scoring list with a third-quarter jumper that stopped a Phoenix run, and his three-pointer early in the fourth started a spurt that put Dallas in control for good.
* At Memphis, Ryan Anderson scored 22 points, connecting on seven three-pointers, and the New Orleans Hornets beat the Grizzlies, 91-83.
Anderson was 7-for-13 from the field, all of his attempts coming from outside the arc. He capped a late New Orleans surge that put the game out of reach, snapping Memphis' two-game winning streak.
Zach Randolph led Memphis with 20 points and 13 rebounds.
* At Orlando, Brandon Knight had a career-high 31 points, including five three-pointers, and Greg Monroe scored 17 points and the Detroit Pistons ended a two-game losing streak with a 104-102 win over the Magic.
The Magic had a chance to tie the game in the closing seconds after a missed free throw, but missed three putback attempts as the final horn sounded.
Orlando's J.J. Redick tied a career high with 31 points and set a career high with eight three-pointers. Jameer Nelson had 18 points and eight assists, and Glen Davis added 17 points and 12 rebounds.
* At Los Angeles, Blake Griffin had team-high 23 points and nine assists as the Clippers snapped a four-game losing streak with a 96-83 win over Portland.