Kidd, 40, and Martin, 35, former team-mates on the old New Jersey Nets, made big rebounds, big steals and clutch plays as the second-seeded Knicks took a 1-0 lead in their best-of-seven Eastern Conference first-round series at Madison Square Garden.
Point guard Kidd made three steals and flung himself to the floor to recover a loose ball late in the fourth quarter to spur the Knicks' charge to victory.
He scored eight points, doled out three assists and hauled down five rebounds, playing more than 35 minutes.
Knicks coach Mike Woodson was not surprised by Kidd's inspirational effort.
"Jason been doing this all season," the Knicks coach said. "Loose balls, strips, keeping balls alive - he just seems to be in the right place at the right time."
Boston coach Doc Rivers could only shake his head in admiration at Kidd, who helped the Dallas Mavericks win the NBA crown two years ago.
"He's just great," said Rivers. "I love watching him. I didn't like watching him today.
"He knows how to play. He says it all the time, 'I'm 40 years old and half the league is faster ... I tell him, not half, 90 percent of the league is quicker and faster.
"He beats everyone with his brain. He beats them into the ground with his brain.
"If you think quicker than a guy can move, you're still quicker. That's why he's there first, because he thought what the guy was going to do before he did it."
Martin, who signed towards the end of the season to return to the NBA wars with the Knicks, supplied rugged defense and a presence down low to pick up the slack for center Tyson Chandler, who is struggling with a bulging disc in his neck.
He played more than 28 minutes, clearing nine rebounds and scoring 10 points, two coming after snaring a bullet pass from Anthony and laying it up and in late in the game.
"It felt like old times," Martin, who is aiming to win his first NBA title, said about teaming up again with Kidd.
"For us to be back here again, I couldn't write it any better, couldn't script it."
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