The Cavaliers have now won 11 consecutive games.
James scored 15 overall in the fourth quarter and strengthened his grip on the NBA lead in fourth-quarter scoring. He entered averaging 9.3 points in the fourth quarter, and it was his jumper with five seconds left that finished the Grizzlies. He added 12 assists in 39 minutes.
Tyreke Evans scored 31 points and added 12 assists for Memphis, which now lost an NBA-high 11 consecutive games.
Marc Gasol added 27 points and six rebounds.
Memphis trimmed what was a 19-point deficit to 93-83 by the end of the third quarter. The Grizzlies got to within three points with 7:37 left in the fourth, and then tied it on Dillon Brooks' 3-pointer with 2:10 to go.
James responded with a bullish post move for a layup, followed by a violent drive to the rim for a layup and a free throw with 34 seconds left.
The Grizzlies led by as many as 12 in the first quarter and were up 32-28 heading into the second. Gasol scored 10 quick points.
A 14-2 run for the Cavaliers starting at the 4:21 mark of the second quarter is when the game turned.
James scored 11 points from that point until the end of the first half and assisted on Cleveland's other two baskets. Dribbling out the clock against Jarell Martin, James turned away from the basket and lofted in a 17-footer at the buzzer for a 66-52 lead.
NOTES: The Cavaliers and G Derrick Rose have held "positive communication" about a possible return, according to cleveland.com. Both coach Tyronn Lue and general manager Koby Altman confirmed the dialogue, but neither would confirm Rose's imminent return. Rose, who has been out since Nov. 9 with complications from a sprained left ankle, left the team Nov. 22 to ponder his basketball future. He was the 2011 NBA MVP, but injuries have since wrecked his career. Altman said there would be news on Rose Sunday, according to cleveland.com. ... Grizzlies G Michael Conley missed his ninth consecutive game due to left Achilles soreness.... Memphis F Chandler Parsons (right ankle, knee) and F/C Brandan Wright (groin) both missed Saturday's game after playing Friday against San Antonio. C Marc Gasol was called "questionable" Saturday morning because of a left foot injury. ... Cleveland's franchise record for consecutive wins is 13, set in 2008-09 and tied the following season. The Cavaliers' next two opponents, the Bulls and Kings, are among the league's worst teams this year.