Edgecombe, who has emerged as one of the league's most efficient performers in "clutch" time - the final five minutes of close games - was named Most Valuable Player of the challenge.
It featured three teams of rookies and second-year players and a team of G League talent in a mini-tournament.
Edgecombe drilled a pair of game-winning free throws as Team Vince beat Carmelo Anthony's Team Melo 25-24 in the rapid-fire championship game in which the first team to 25 points won.
San Antonio's 2025 Rookie of the Year Stephon Castle had put Team Melo up 24-23 with a tip-in dunk, but Donovan Clingan fouled Edgecombe on the other end, and the 20-year-old from the Bahamas closed it out.
Edgecombe, the third overall pick in the 2025 draft, had delivered the game-winner in his team's 41-36 win over Tracy McGrady's Team T-Mac to reach the title contest.
In the other semi-final - both played to 40 points - Team Melo closed with a 12-2 scoring run to beat the team of G League players coached by Austin Rivers 40-34.
San Antonio rookie Dylan Harper, the second overall pick in the 2025 draft, closed out that win with a step-back basket over his brother Ron Harper Jr. - a G League regular who has played for the Boston Celtics on a two-way contract this season.
Like Sunday's All-Star Game proper, the Rising Stars Challenge at the Intuit Dome - home of the Los Angeles Clippers - was hit by injuries.
Dallas rookie Cooper Flagg, the top overall pick in the 2025 draft, was ruled out with a sprained foot.
The All-Star festivities continue on Saturday with the Slam Dunk Contest, the Three-Point Contest, and the Skills Challenge.