Kentavious Caldwell-Pope scored 15 points and Brook Lopez added 15 points and 10 rebounds for the Lakers (6-8), who ended a three-game losing streak in a game where neither team had a double-digit lead until 2:30 remained.
Brewer finished with 13 points and Kuzma had 11 points for the Lakers, who have two of their six wins against the Suns in Phoenix.
Devin Booker had 36 points for Phoenix, his sixth 30-plus-point performance in the first 15 games of the season. TJ Warren had 21 points and Dragan Bender had a career-high 15 for the Suns (5-10), who have lost six of their last seven games.
Phoenix was within two points at 85-83 on a Booker jumper with 5:58 left. But Kuzma hit two 3-pointers and Brewer one to spark a 9-1 run and give the Lakers some breathing room at 94-86 with 4:11 left.
Booker and Warren, who each scored 35 points in a win over the Minnesota Timberwolves on Saturday, combined for the first nine points Monday and 14 of 20 Phoenix points in the first quarter.
But the early 9-0 lead lasted less than two minutes and Phoenix didn't have a field goal for the final four minutes. Clarkson's bank shot with 42.4 seconds left gave the Lakers a 21-20 lead after one.
Booker scored 13 more points in the second quarter, including 10 in the first six minutes and seven during a 13-2 run that put the Suns up 39-33 with 4:14 left.
But the Lakers rallied again before halftime. Caldwell-Pope had five of his 11 first-half points in the final 3:09 and the Suns needed a Booker 8-footer with 2.3 seconds left to take a 44-43 halftime lead.
Booker, Warren and Bender were a combined 17 of 30 in the first half while the other seven Suns who played were 1 of 19.
NOTES: Only one other Suns player has accomplished G Devin Booker's feat of scoring at least 30 points in six of the first 15 contests. Charlie Scott did it in both 1972-73 and 1974-75. ... Lakers G Lonzo Ball became the youngest player in NBA history to record a triple-double, when he had 19 points, 13 assists and 11 rebounds on Saturday at 20 years and 15 days old, five days younger than LeBron James. Magic Johnson had been the youngest Laker to accomplish the feat at 20 years, 75 days. ... Phoenix interim coach Jay Triano stuck with Tyler Ulis as a starting point guard over Mike James for a second straight game.