Richard Jefferson had 26 points, 6 rebounds and 5 assists and Vince Carter had 20 points as the Nets (2-4) blew a late 13-point lead but came back to win their second exhibition game in a row.
Sebastian Telfair, who rolled his right ankle midway through the fourth quarter, led the Celtics' comeback with 9 of his 21 points in the final 1:08. He hit two game-tying free throws with 7.8 seconds to play after being fouled by Walsh.
After a time out, Walsh got the ball on the left wing and was fouled by Gerald Green on a drive to the basket. His free throws were his only points, and they snapped a two-game winning streak by the Celtics (3-4).
Allan Ray was knocked down on a drive to the basket in the final seconds, but no foul was called.
Nenad Krstic finished with 16 points and 8 rebounds for New Jersey. Jason Kidd added 12 assists and top draft pick Marcus Williams had 11 points in his first action since missing two games with a wrist injury.
Wally Szczerbiak scored 16 points and Tony Allen had 15 for the Celtics. Ryan Gomes added 14 points and Al Jefferson and Rajon Rondo had 13 apiece.
The Nets seemed to take control midway through the fourth quarter with a 20-7 spurt that featured consecutive three-point plays by Carter and four points apiece by Williams and Mikki Moore. A hook shot by Moore gave New Jersey a 107-94 lead with 2:22 to play.
The Celtics were missing swingman Paul Pierce. The NBA's sixth-leading scorer last season (26.8 points) returned to Boston earlier in the day to get treatment for an infected middle finger on his left hand.