Kuzma was four of six from behind the three-point line as the Lakers won their eighth straight game.
The Lakers led by as many as 32 points in the second half, but the Thunder cut the lead to just 11 with less than three minutes remaining before Kuzma drained back-to-back shots to give the Lakers control again.
James was ruled out after succumbing to a cold.
James shrugged off the early symptoms of his illness on Friday to lead the Lakers to an emphatic 129-114 win over the Dallas Mavericks, scoring 35 points and grabbing 16 rebounds to set up the victory.
However the Lakers confirmed on Saturday that the veteran would miss the team's road game against the Thunder.
Teammate Davis also didn't play after suffering a bruised tailbone on Tuesday.
James' display on Friday saw him move up into fourth place on the leaderboard for all-time field goals, moving clear of Michael Jordan.
James has led a resurgence of the Lakers this season, with his performances propelling them to the top of the Western Conference with 31 wins and only seven defeats.