James scored 30 points on 11 for 15 shooting and Dwyane Wade added 24 points for Miami, which wasted a pair of 14-point leads – then put the game away with a 14-0 run in the final minutes. Ray Allen added 14 for Miami.
Damian Lillard had a game-high 33 points for Portland, which got 29 from LaMarcus Aldridge and 20 from Wesley Matthews.
It was the 1,000th regular-season win in Heat history. But on this night, the only history anyone will remember was what James accomplished.
“I’m at a loss for words,” James said in a televised postgame interview. “Like I say over and over, I know the history of the game. I know how many unbelievable players who came through the ranks, who paved the way for me and my teammates. And for me to be in the record books by myself with such a stat – any stat – it’s big-time.”
RAPTORS 109, NUGGETS 108
In Toronto, Rudy Gay hit a pull-up jump shot with less than five seconds remaining and Toronto beat short-handed Denver.
DeMar DeRozan scored 22 points, Gay had 17 and John Lucas scored 12 of his 14 points in the final quarter as the Raptors won their third in a row.
It was the second game-winner in three games for Gay, who beat Indiana with an overtime jumper last Friday.
Kyle Lowry had 11 points and 10 assists and Alan Anderson had 10 for Toronto, which made seven 3-pointers in the fourth quarter.
GRIZZLIES 108, KINGS 101
In Memphis, Tenn., Marc Gasol had 24 points and 12 rebounds, Mike Conley scored 22 points and Memphis beat Sacramento.
Tony Allen added a season-high 19 points to help the Grizzlies win their sixth straight over the Kings at home.
Memphis entered the All-Star break with a three-game win streak, their longest in more than a month.
DeMarcus Cousins scored 23 points and Tyreke Evans had 20 for the Kings.