The red-hot Lakers extended their unbeaten streak to eight games in a pulsating battle at the Crypto.com Arena that saw Doncic finish with 32 points while James poured in 31.
Doncic and James had both been instrumental in dragging the Lakers back into the contest after the Knicks led by 10 points midway through the fourth quarter.
The Knicks meanwhile were left ruing a potential victory that slipped through their fingers despite a majestic performance from Jalen Brunson, who scored a game-high 39 points.
The agony of the Knicks' defeat was compounded by an injury to Brunson in overtime, with the mercurial point guard limping off the court after rolling his right ankle in a collision with the Lakers' Austin Reaves.
"Our physicality in the fourth quarter was next level," an exhausted Doncic said afterwards. "Once we got started, we played basketball.
"They're a great team with great players and it's a tough win. We've got eight in a row now and every game is a battle for us."
The Lakers looked to be struggling after trailing for most of the game against a fired-up Knicks, who led by as much as 13 at one stage.
But after struggling for shooting accuracy for most of the contest, the Lakers began making shots in the fourth quarter. James bagged a crucial pair of three-pointers while Gabe Vincent also drained three from outside the arc to spark the comeback.
Vincent finished with 12 points while Lakers rookie Dalton Knecht also chipped in with 11 points off the bench, including three three-pointers.
The Lakers moved to 40-21 with the victory to remain in second place in the Western Conference, 10.5 games adrift of runaway leaders Oklahoma City.
Nets 119-121 Warriors
Elsewhere, Curry - who scored 28 points in the Warriors' comeback victory over the New York Knicks on Tuesday - was in superb form as Golden State climbed out of a 22-point first-quarter hole to grab a third consecutive road win.
Curry's 40-point haul included seven three-pointers from 13 attempts, with the pick being a jaw-dropping heave from near halfway to end the first half.
That highlight reel-worthy moment made it a five-point game at the break as the Warriors roared back to life after being outscored by a whopping 35-15 in the first quarter.
The Warriors found their rhythm in the second period, pouring in 40 points to the Nets' 25 before going on to complete the comeback after the interval.
Curry was backed by 25 points from Jimmy Butler while Gary Payton II added 16 from the bench. Cameron Johnson led Brooklyn's scoring with 26 points.
The Warriors improved to 35-28 and are now sixth in the Western Conference as they chase a return to the postseason after missing out last year.
Celtics 123-105 76ers
The Boston Celtics maintained their pursuit of the Cleveland Cavaliers at the top of the Eastern Conference after cruising past an injury-depleted Philadelphia 76ers.
The Sixers, missing Joel Embiid, Paul George and Tyrese Maxey, were never in the hunt as the Celtics completed a wire-to-wire victory to improve to 45-18 in the East, 7.5 games back from leaders Cleveland.
Jayson Tatum led the rout for Boston with 35 points, while the in-form Payton Pritchard came up big from the bench with 19 points.
The only down note for the Celtics came in the second quarter when Derrick White was forced to leave the game after losing a tooth in a physical tussle with the Sixers' Kelly Oubre Jr.
White left the game but returned in the second half wearing a mouthguard.
Around the league
In other games on Tuesday, the Atlanta Hawks downed the Indiana Pacers 124-118 while the Chicago Bulls outmuscled the Orlando Magic 125-123. In New Orleans, the Houston Rockets overpowered the Pelicans 109-97.
