Reaves, an undrafted first-year pro who impressed enough in the off-season to gain a two-year contract with the Lakers, drained a game-winning three-pointer as time expired to give Los Angeles a third straight win.
The 23-year-old was mobbed by teammates, and superstar LeBron James said the team had no hesitation in handing the ball to the relative unknown.
"Listen, we've got a lot of trust in whoever is on the floor, including the rook," James said. "And, obviously, it showed on that last possession."
Reaves's fifth three-pointer of the night saved the day after a late string of misses endangered the Lakers' chances in a game that featured 19 lead changes and was a battle all the way.
"There was about two seconds left, so I didn't really have anything else to do but shoot it," Reaves said.
The rest of the Lakers' 14 points in overtime came from their big three of James, Westbrook and Anthony Davis.
James finished with 24 points. Westbrook scored 23 with 10 rebounds and nine assists and Davis added 20 points and 12 rebounds in his first game back after missing two with a sore left knee.
Jalen Brunson scored 25 points and Kristaps Porzingis scored 23 points and pulled down 12 rebounds for Dallas, whose star guard Luka Doncic missed a third straight game with left ankle trouble.
The Lakers were without three players who were in Covid-19 health protocols in a week in which coronavirus again became a major factor in the NBA as well as other US sports.
Multiple teams saw players sidelined. The Chicago Bulls had two games postponed because they couldn't field a minimum eight players. The Nets had won with the minimum on Tuesday.
"I'm worried," Philadelphia 76ers coach Doc Rivers said before his team's 101-96 home loss to the Miami Heat. "I'm just worried in general.
"I see football and hockey and us -- there's just a lot of it right now. There's a lot of it nationwide, outside of sports as well."
Philadelphia were buoyed by the return from injury of center Joel Embiid, who had 17 points and 14 rebounds, but the short-handed Heat put them away in large part thanks to a barrage of 18 three-pointers.
The Heat had only 10 available players thanks to injuries, illness and Covid-19 absentees. Those missing included their three top scorers in Jimmy Butler, Tyler Herro and Bam Adebayo.
But Gabe Vincent stepped up with a career-high 26 points, draining a clutch three-pointer that put Miami up 99-96 with 39.4 seconds left in the fourth quarter.
He made seven three-pointers and Duncan Robinson made four on the way to 21 points as Miami seized control early, leading by as many as 10 points in the first half and pulling ahead by 23 in the third.
The Milwaukee Bucks were without two-time NBA Most Valuable Player Giannis Antetokounmpo because of Covid protocols and without Khris Middleton because of injury.
But the reigning NBA champions had 26 points from Jrue Holiday and put together a 21-0 fourth-quarter scoring run to break open a close game and beat the Indiana Pacers 114-99.
Pacers coach Rick Carlisle missed his third game since he tested positive for Covid-19.
In Denver, Anthony Edwards hit a career-high 10 three-pointers on the way to 38 points to lead the Minnesota Timberwolves to a 124-107 victory over the Nuggets.
Charlotte's Gordon Hayward scored a season-high 41 points in leading the Hornets to a 131-115 wire-to-wire victory over the San Antonio Spurs.
It was a wild finish in Oklahoma City, where New Orleans' Devonte' Graham's desperate heave from 61 feet dropped to give the Pelicans a 113-110 victory over the Thunder at the buzzer.
The Utah Jazz won their eighth straight, downing the Los Angeles Clippers 124-103.
Donovan Mitchell scored 27 points, Rudy Gobert scored 20 points and grabbed 17 rebounds and Bojan Bogdanovic connected on six of seven three-point attempts on the way to 20 points as the Jazz pushed their record to 20-7.