Dazzling from inside and out, LeBron James put on the best scoring show of his N.B.A. career on Monday night, pouring in 61 points — a career best and a franchise record — as the Miami Heat beat the visiting Charlotte Bobcats, 124-107. James made 22 of 33 shots from the field, including his first eight 3-point attempts, on his way to the historic night. “The man above has given me some unbelievable abilities to play the game of basketball,” James said. “I just try to take advantage of it every night. I got the trust of my teammates and my coaching staff to go in there and let it go.” His career best had been 56 points, on March 20, 2005, for Cleveland against Toronto. Glen 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 minutes 46 seconds left, when James spun around three defenders for a layup that fell as he tumbled to the court. “There was an efficiency to what he was doing,” Heat Coach Erik Spoelstra said. “The rim looked like an ocean for him.” When James checked out with 1:24 left, the entire Heat roster met him near midcourt for high-fives and hugs, and the crowd gave him a standing ovation. Charlotte has allowed the two highest scoring totals in the N.B.A. this season. Carmelo Anthony had 62 points for the Knicks against the Bobcats on Jan. 24. Chris Bosh scored 15 for the Heat, and Toney Douglas added 10. Al Jefferson had 38 points and 19 rebounds for the Bobcats, although his huge night was an afterthought. Miami, which won its eighth straight, was without guard Dwyane Wade, who got a night off to rest. Spoelstra stressed that there had been no setback for Wade, who has been on a knee-maintenance program throughout this season.