Walker, who scored 14 points, was not the highest scorer for the visitors, though as Jayson Tatum scored 23 and Gordon Hayward finished with 20 as the Celtics extended their winning streak to six.
Miles Bridges claimed 18 points and 10 rebounds for the Hornets, who ended their three-match winning run.
Walker, who is the Hornets' all-time leading scorer, is still highly regarded by the Charlotte fans and received a one-minute standing ovation that left the point guard in tears.
Phoenix are now 5-3 and currently sit in fifth place in the Western Conference.
His team-mate Dejounte Murray also had a good night, with a career-high 10 assists along with 17 points and eight rebounds.
The Spurs are now 5-3 and in eighth place in the Western, while the loss sees Thunder on 3-5 and in 11th place.
In the final game of the night, the LA Clippers beat the Portland Trail Blazers 107-101.