The Lakers fought back from a 19-point deficit in the third quarter, helped in part by James who added eight and pushed LA ahead of the Rockets with four minutes and fifteen seconds remaining.
As well as his sizeable points haul James had 11 rebounds and six assists, while Brandon Ingram scored 27, with 13 rebounds and one assist.
James Harden led Houston with 30 points, five rebounds and six assists, while Chris Paul added 23, with 10 rebounds and nine assists.
Steph Curry racked up three dozen points, while Kevin Durant added 28 as the Golden State Warriors held on to edge past the Sacramento Kings 125-123.
Curry scored 11 of his points in the fourth, which saw the teams separated by no more than six at any one time.
Elsewhere the Cleveland Cavaliers saw off the Phoenix Suns 111-98 and the Philadelphia 76ers beat Miami Heat 106-102.
The Portland Trail Blazers defeated the Brooklyn Nets 113-99 and the Milwaukee Bucks won their game against the Boston Celtics 98-97.