Reaves' basket, his fifth from behind the arc on six tries, came from 25 feet on a kickout from Russell Westbrook. He had the Lakers' only overtime points scored by someone other than the team's Big Three of LeBron James, Anthony Davis and Westbrook.
"There was about one second left, and I didn't have anything to do but shoot it," said Reaves, who played two seasons each at Wichita State and Oklahoma, signing a two-way contract with the Lakers in August that was converted to a regular contract in September. "Great pass, and I made a shot."
James scored 24 points, Westbrook added 23 and Davis had his sixth double-double of the season with 20 points and 12 rebounds after missing two games with a sore left knee.
But it was the undrafted player who made sure they left with a victory.
"We've got a lot of trust in whoever's on the floor, including the rook," James said. "Obviously, it showed on that last possession."
Jalen Brunson scored 25 points and Kristaps Porzingis had his eighth double-double this season with 23 points and 12 rebounds for the Mavericks, who played their third straight game without All-Star guard Luka Doncic.
"Man, it sucks," Porzingis said, rubbing his face. "Oh, my god. We should have got this one."
Brunson said he'd seen Reaves play in college.
"He has game," Brunson said. "You've got to respect him, and he was able to make shots."
A 3-pointer by Westbrook gave the Lakers a 104-101 lead with 23.5 seconds left in overtime. Maxi Kleber tied the score with 15.2 left when he banked in a shot from 25 feet.
Los Angeles' final possession didn't follow Dallas' defensive plan.
"We were going to foul with 10 seconds, make them reset and gives us a chance to reset, too," said Mavericks coach Jason Kidd, who was a Lakers assistant during the past two seasons. "And we just didn't get to the foul."
James for 4 of 9 on 3-pointers, including a 35-foot swish near the midcourt logo in the third period.
Three Lakers were missing after entering the NBA's COVID-19 protocol: center Dwight Howard, forward Talen Horton-Tucker and guard Malik Monk. Two of the 36-year-old Howard's three starts this season came in the last two games with Davis out. Horton-Tucker scored a career-high 19 points in Sunday's win over Orlando.
LA STAFFING ISSUES
Other members of the Lakers' traveling party who entered the virus protocol included assistant coach Phil Handy and TV play-by-play announcer Bill Macdonald. Assistant coach David Fizdale missed the game for what the team called personal reasons unrelated to COVID.
"It's the same thing you tell your players - next man up," coach Frank Vogel said of filling in for two assistants. "Everybody's prepared to the job of the guy in front of him."
Lakers: Wayne Ellington made his third start of the season and scored nine points in 38 minutes, including the 3-pointer from the left corner that sent the game into overtime. ... Davis played 14 first-half minutes with four points, five rebounds, five turnovers and three fouls.
Mavericks: They're 2-5 without Doncic, who will also miss Dallas' next game on Sunday at Minnesota. ... The Mavericks outscored the Lakers 14-0 on second-quarter points in the paint with Brunson going 6 for 7. ... Willie Cauley-Stein missed his 10th consecutive game for personal reasons. Sterling Brown missed his sixth straight game with a foot injury.
Lakers: At Minnesota on Friday.
Mavericks: Sunday's game at Target Center will begin a home-and-home with the Timberwolves.
Austin Reaves splashes winning 3 for Lakers in final second of OT
Austin Reaves nails the 3-pointer right before the overtime buzzer, giving the Lakers a three-point win over the Mavericks.