Memphis has lost 11 in a row, including three since David Fizdale was fired Monday and replaced by interim coach J.B. Bickerstaff.
The Grizzlies trailed 91-72 late in the third quarter, but rallied all the way to a tie at 109 on Dillon Brooks' 3-pointer with 2:10 remaining. James' basket in the lane gave Cleveland the lead.
After Tyreke Evans missed a 3-pointer, James drove the lane, scored and converted the three-point play after being fouled by Brooks with 34 seconds left.
Brooks made two free throws, but James dribbled for several seconds on Cleveland's next possession and hit a jumper from the top of the key for a five-point lead with 5 seconds to go.
Evans had 31 points and 12 assists for Memphis. Marc Gasol scored 27 and passed 10,000 career points despite being listed as questionable after injuring his left foot in Friday's loss to San Antonio.
Cleveland has scored at least 100 points in each game during its streak and is closing in on its longest winning streak since it ripped off 12 straight in 2015.
James scored 11 points in the final six minutes of the second quarter, including a pair of three-point plays and a jumper from the corner at the buzzer, helping Cleveland to a 66-52 halftime lead.
James, the reigning NBA Player of the Month, also had 12 assists. He has shot 50 percent or better from the floor in each of his last 10 games.
Kevin Love added 20 points and 11 rebounds for Cleveland. He went to the floor after banging knees with JaMychal Green in the third quarter, but remained in the game.
Memphis point guard Mike Conley missed his ninth straight game because of a sore left Achilles.
CAVS, ROSE TALKING
Cleveland coach Tyronn Lue said the team's communication with point guard Derrick Rose has been positive. Rose is away from the team because of a personal matter. He also has been sidelined by a sprained left ankle. The team is expected to provide another update Sunday.
Grizzlies: Gasol has 10,007 career points. ... Memphis hit seven of its first nine shots and took a 16-9 lead, forcing the Cavaliers to call a timeout four minutes into the game. Cleveland called another timeout at the 4:24 mark with Memphis leading 24-13. ... Memphis didn't get to the line until Evans was fouled shooting a 3-pointer at the 6:50 mark of the second quarter.
Cavaliers: J.R. Smith scored 17 points, and Dwyane Wade had 16. ... Love was the only starter to get a rebound in the first half when he had seven. ... F Channing Frye went to the locker room in the fourth quarter with an apparent hand injury, but returned to the bench.
Grizzlies: Host Minnesota on Monday. Memphis has lost eight straight at FedEx Forum.
Cavaliers: Visit Chicago on Monday. Cleveland defeated the Bulls 119-112 on Oct. 24 in Cleveland.
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