When the New York Knicks were constructing a supporting cast to surround scoring superstar Carmelo Anthony last offseason, they targeted a specific type of player.

“I was basically looking for guys that had a defensive attitude and a little edge about them,” Knicks coach Mike Woodson said.

In other words, Woodson wanted players like Jason Kidd. It was a match for both sides, and the 40-year-old kid signed a three-year, $9 million free agent contract with the Knicks.

Kidd’s regular-season stats were underwhelming, as he averaged 6.0 points, 4.3 rebounds and 3.3 assists. But the signing was validated Saturday, when Kidd had eight points, five rebounds, three assists and three steals in the Knicks’ 85-78 win over the Celtics in Game 1 of their Eastern Conference quarterfinal series.

“It’s just being lucky,” said Kidd, who won a title with the Dallas Mavericks in 2011. “Understanding what is at stake and who is behind me and being at the right place at the right time.”

Kidd made a profound impact in the fourth quarter without scoring a point. He had three steals and held his ground while defending Paul Pierce. Kidd’s signature play came with 4:48 remaining, when he stole a Jeff Green pass and then dived on the loose ball to start a Knicks break.

“He has a champion’s heart,” Knicks center Tyson Chandler said. “That play when he got his hands on the ball, dove for it and came up with it, that was a key possession. A 40-year-old stripping the ball and diving on the floor for it is key. He is one of the greats and it’s good to witness it right now.”