Rice scored 56 to set the Heat record on April 15, 1995, against Orlando.
James had 24 points at halftime, then added 25 in the third quarter. The record-breaker came with 5:46 left, when James spun through three defenders for a layup that fell as he tumbled to the court.
Al Jefferson had 38 points and 19 rebounds for the Bobcats, his huge night merely an afterthought.
When James checked out with 1:24 left, the entire Heat roster met him near midcourt for high-fives and hugs, and the sellout crowd gave him a standing ovation. A second huge roar followed when he waved to the crowd, as "M-V-P" chants rained down.
Charlotte has allowed the two biggest single-game scoring totals in the NBA this season. Carmelo Anthony had 62 points for the New York Knicks against the Bobcats on Jan. 24.
Miami was without guard Dwyane Wade, who got a night off to rest.
NETS 96, BULLS 80
NEW YORK • Jason Collins played the final minutes of a winning home debut with the Brooklyn Nets, who cooled off Chicago.
Finally playing at home more than a week after returning to the NBA as the league's first openly gay player, Collins checked in with 2:41 remaining to a standing ovation from a sellout crowd of 17,732 that included former NBA Commissioner David Stern. Collins committed a foul just 5 seconds later and missed his only shot as the Nets won their third straight.
Collins' original 10-day contract will expire Tuesday and the Nets plan to sign him to a second deal on Wednesday. He has appeared in all five games since he signed on Feb. 23.
Deron Williams scored 20 points and Joe Johnson had 19 for the Nets (29-29), who got back to .500 for the first time since they were 2-2 on Nov. 5.
The sloppy Bulls turned it over 28 times, leading to 30 Brooklyn points, and had their four-game winning streak snapped. They had a franchise-low three turnovers in their 109-90 victory over the Knicks on Sunday and had won nine of 10.
GRIZZLIES 110, WIZARDS 104
WASHINGTON • Tayshaun Prince scored a season-high 21 points and Memphis withstood a late rally to snap Washington's winning streak at six.
Zach Randolph added 16 points and 10 rebounds for the Grizzlies, who improved to a season-high nine games above .500 and pulled within one game of the eighth and final playoff spot in the Western Conference. Memphis shot 60 percent after the first quarter and outscored Washington 62-34 in the paint for the game.
John Wall scored 23 points and Bradley Beal had 21 for the Wizards. Washington had answered a challenge by winning its first three games after losing starting forward Nene to a knee injury, but this time the rotation was also missing forwards Kevin Seraphin (sore right knee) and Martell Webster (sore back).
TIMBERWOLVES 132, NUGGETS 128
DENVER • Kevin Love scored 33 points and tied a season high with 19 rebounds for his NBA-best 50th double-double this season, and Minnesota beat skidding Denver for its third win in a row.
Love topped 30 points for the 11th time in his last 14 starts, helping the Timberwolves wrap up a 4-1 trip out west.
The Nuggets got a boost from the return of Ty Lawson, who scored a season-high 31 points with 11 assists in his first game since breaking his left rib Feb. 8 at Detroit. But it wasn't enough to reverse their sagging fortunes. Denver lost its sixth straight and has dropped 11 of 12 overall.
Kevin Martin added 22 points for the Timberwolves, including four clutch free throws in the final 11.7 seconds. Minnesota finished with a huge advantage at the foul line, making 52 of 64 (81.3 percent) to Denver's 16 of 25 (64 percent).
LAKERS 107, TRAIL BLAZERS 106
PORTLAND, Ore. • Kent Bazemore threw an alley-oop to Wesley Johnson for the go-ahead dunk with 6.9 seconds left to lift Los Angeles over Portland.
Pau Gasol scored 22 points and the Lakers won their second straight, snapping the Trail Blazers' five-game winning streak. Jodie Meeks added 21 points.
The Lakers led by 15 in the first quarter and pushed the lead to 97-86 in the fourth, but Wesley Matthews' fadeaway jumper tied it at 105 with 1:10 left.
Damian Lillard hit one of two free throws to give Portland its first lead since the first quarter. But the officials reversed a possession call with 7.1 seconds left, giving the ball to the Lakers. Bazemore lobbed to Johnson for the dunk and Lillard missed a 3-pointer as time ran out.
Robin Lopez had 19 points and 16 rebounds for the Blazers.
PISTONS 96, KNICKS 85
AUBURN HILLS, Mich. • Andre Drummond had 17 points and a career-high 26 rebounds as Detroit surged past New York in a matchup of slumping teams.
The Pistons had lost four straight and seven of eight. New York has dropped seven straight and 13 of 15.
Carmelo Anthony scored 10 of his 28 points in a first quarter in which the Knicks led by as much as 14.
Detroit reserves Rodney Stuckey and Will Bynum each scored 16 points, helping their team's bench outscore New York's 36-7. The Pistons started the fourth quarter with eight unanswered points.
Amare Stoudemire had 22 points for the Knicks despite playing sparingly in the fourth quarter.
KINGS 96, PELICANS 89
SACRAMENTO, Calif. • DeMarcus Cousins had 23 points and 12 rebounds, Isaiah Thomas scored 22 and Sacramento beat slumping New Orleans.
Behind the scoring of Thomas, the Kings took the lead late in the third quarter and never trailed in the fourth while snapping a three-game losing streak.
Rudy Gay added 14 points and Reggie Evans had 10 points and 13 rebounds for Sacramento, which outrebounded the Pelicans 47-30.
Tyreke Evans scored 14 of his 27 points in the fourth quarter and added 10 rebounds and eight assists for the Pelicans, who have dropped eight straight and 10 of 11.
New Orleans All-Star forward Anthony Davis shot 4 of 14 and had 13 points. He missed his first 10 shots.