Russell Westbrook led Los Angeles with 29 points off the bench and superstar LeBron James added 23 for a Lakers team that has struggled to find consistency amid injuries -- including the foot trouble sidelining Anthony Davis.
But it was German guard Schroder who starred late, serenely draining a pair of free throws to pull the Lakers within one -- at 120-119 -- with 13.2 seconds left.
On Memphis' ensuing possession he poked the ball away from Desmond Bane and raced up the court with it for a layup. Fouled on the play, he made the free throw to put the Lakers up 122-120.
The Grizzles would have another chance, but Ja Morant missed a driving shot and Brandon Clarke missed one of two free throws and the Lakers had the win.
Morant shook off a slow start to lead Memphis with 22 points. Tyus Jones and John Konchar had 20 each off the bench, but the Grizzlies slipped a game and a half behind Western Conference leaders Denver, who beat Indiana 134-111 for their ninth straight victory.
It was just the second time this season the Grizzles lost when leading after three quarters -- and just the second Lakers' win when trailing through three.
But it wasn't the only unlikely outcome on the night as Jordan Poole and Golden State put on a shooting clinic in Cleveland, the Warriors draining 23 three-pointers in a 120-114 victory with Stephen Curry and three other starters on the bench.
Curry, Klay Thompson, Andrew Wiggins and Draymond Green all sat out the contest a day after the NBA champions' heartbreaking overtime loss to the Celtics in Boston.
But with 32 points from Poole and 22 from Ty Jerome the Warriors posted their first road victory this season over a team with a winning record.
The Warriors set the tone early, connecting on seven of eight three-pointers in the first quarter. Their 14 first-half three-pointers matched the most ever by a Cleveland opponent for one half.
Golden State pushed a five-point halftime lead to as many as 20 in the third. Cleveland sliced the deficit to four with two minutes remaining, but Jerome promptly drained another three-pointer and the Warriors were off again.
Warriors coach Steve Kerr was unrepentant about sitting his starters, saying banged up players had to be given a chance to rest or risk injury.
Darius Garland scored 21 to lead Cleveland, who were again without three-time All-Star Donovan Mitchell because of a groin injury.
Murray leads Denver
In Denver, two-time reigning MVP Nikola Jokic was sidelined with a hamstring injury.
But teammate Jamal Murray scored 17 points with 14 assists and 10 rebounds for the first triple-double of his career to lead the Nuggets over the Pacers.
In Dallas, the Mavericks' MVP candidate Luka Doncic scored 34 points -- making five of his eight three-point attempts -- with 12 rebounds and seven assists in a 115-90 rout of the Miami Heat.
Brooklyn's Kyrie Irving put on a show in Salt Lake City, scoring a season-high 48 points to lead the Nets to a 117-106 victory over the Utah Jazz.