Kidd bumped into and briefly argued with Woodson, the spark Dallas needed to overcome a 15-point deficit in the fourth quarter and beat Atlanta 111-103 in overtime on Friday night.
"The coach is not supposed to be on the floor," Kidd said. "You see that a lot in games. The NBA has so many rules, and there is a coaching box, and some of the coaches do stretch that box. For me, it's just a reaction. Make something happen. It was a big play for us."
Dirk Nowitzki scored 37 points, Kidd had 19 points, 17 assists and 16 rebounds, and the Mavericks won their sixth straight.
Kidd had his first triple-double this season and 104th of his career, third-most in NBA history behind Oscar Robertson and Magic Johnson.
"This one, I will treasure as much as the first one I had," Kidd said. "At 36, I feel great. A triple-double at 36 is special."
Joe Johnson scored 27 points for Atlanta, which dropped to 22-7 at home. The Mavericks won their Western Conference-best 19th on the road, one more than their total last season.
Josh Smith forced overtime with a putback that tied it at 99.
With 1:37 left in regulation, Kidd bumped into Woodson after the Atlanta coach took too long to step off the court as the guard was dribbling near the left sideline.
"I said, 'You can't be on the floor. You don't have a uniform on,"' Kidd said. "It was just a play. We move on."
Woodson seemed to be pulling his right foot off the floor when Kidd used his left arm to push the coach back rather softly into the scorer's table.
"The officials got it right," Kidd said. "I thought from there, mentally, we took control of the game. That play just presented itself. It's just a reaction and just understanding what the team needs. Rules are rules. The coach isn't supposed to be on the floor."
Lead official Mark Wunderlich quickly called timeout, cleared the players from the floor and brought Dallas coach Rick Carlisle over to speak with Woodson before whistling the Atlanta coach for a technical foul.
After Nowitzki hit the ensuing free throw that cut the Atlanta lead to 97-96, Johnson missed a jumper before Kidd hit a 3 in front of the Hawks' bench to put Dallas ahead 99-97.
Woodson later credited Kidd with being alert.
"He made a heck of a play," Woodson said. "Jason Kidd is an All-Star. He's a [potential] Hall of Fame guard. He's had a hell of a career. He did what he had to do. Unfortunately, it didn't turn out to favor the team. I've got to take the hit for that."
Atlanta missed its first eight shots of overtime before Smith's layup cut the lead to 108-103 with 30 seconds remaining.
Hawks sixth man Jamal Crawford hit a pair of free throws with 8:23 left in regulation to make it 86-71 for the game's biggest lead. But he and his teammates soon lost their shooting touch, as Crawford combined with Al Horford, Mike Bibby and Marvin Williams to finish just 17 for 54 from the field.
"They were smart enough to stay in the zone [defense] until late in the game," Crawford said. "When they [switched], we were up 13 in the fourth quarter. We got some great shots. Shots that, if we came in here tomorrow, we'd knock down most of them."
Nowitzki hit 15-of-26 shots for the Mavs, and teammate Shawn Marion finished with 14 points after going 7 for 11 from the field.
The story, however, was Kidd, who had nine points, four rebounds, three assists and one steal in the final 4:53.
"Well, it wasn't at first," Kidd said. "I missed a lot of open shots and I thought I was letting my teammates down."
- Kidd's rebound total was a season high, and his assist total tied a season high.
- Mavs F DeShawn Stevenson, who started his second straight game because Caron Butler is having a negative reaction to medication, finished with three points.
- Dallas improved to 22-6 when scoring 100-plus points and 22-5 when outrebounding opponents.
- Smith's seven steals were a career high.