Phoenix, missing top scorer Devin Booker due to a groin injury, improved to 14-10 by snapping the Timberwolves' five-game win streak with Mark Williams scoring 22 points to top six double-digit scorers for the Suns.
The Spurs, still without French star Victor Wembanyama due to a left calf strain that has caused him to miss 11 games, got 24 points from Harrison Barnes and 22 from reserve Dylan Harper to defeat the host Pelicans.
The Suns (14-10) and Spurs (16-7) won their final matchups ahead of NBA Cup quarterfinal games on Wednesday, with San Antonio at the Los Angeles Lakers and Phoenix at Oklahoma City, where the host Thunder, an NBA-best 23-1, will try to stretch their 15-game overall win streak.
The NBA Cup quarter-finals begin on Tuesday with Miami at Orlando and New York at Toronto.
At Phoenix, the Suns also had 19 points from Collin Gillespie and 18 from Dillon Brooks, who was nagged by a sore left Achilles tendon.
An inside shot by Edwards with 8.9 seconds remaining lifted Minnesota (15-9) within 106-105, but Gillespie hit two free throws with 6.3 seconds to play, and Minnesota's Jaden McDaniels missed a tying three-point shot to seal the T-Wolves' fate.
At New Orleans, Harper's layup with 9.1 seconds remaining lifted San Antonio ahead 133-132.
Derik Queen - who delivered a triple-double of 33 points, 10 rebounds, and 10 assists for New Orleans - missed a jumper with 3.8 seconds remaining, then fouled De'Aaron Fox, who sank two final free throws.
Saddiq Bey missed a potential tying three-pointer at the buzzer as the NBA-worst Pelicans fell to 3-22 with their seventh loss in a row.
San Antonio guard Stephon Castle, who missed the past three weeks with a hip injury, made his return and contributed 18 points, five rebounds, and five assists.
In Monday's only other game, the Indiana Pacers beat visiting Sacramento 116-105.
Andrew Nembhard led Indiana (6-18) with 28 points and 12 assists, while Bennedict Mathurin added 25 points and Pascal Siakam had 23.
Russell Westbrook had a triple-double for the Kings (6-18) with 24 points, 14 assists, and 13 rebounds.