Newman approached the Joe Gibbs Racing driver about 10 minutes after the 200-lap event as the two were leaving the garage. The Stewart-Haas driver apparently was upset over an incident on Lap 148 in which the 20-year-old Logano got into the back of his car in Turn 4.
Newman, who began the day 14th in points and 83 behind the 12th spot for the Chase, spun out. He finished 23rd to fall 103 points behind the final playoff position with three races to go.
NASCAR officials stepped into the argument when it appeared Logano brushed Newman with his hand.
"Don't touch me! Don't touch me!" Newman said.
Newman declined to comment to reporters afterwards, but as officials separated the drivers he said, "I'm just trying to teach the little kid how to drive."
The confrontation began with Newman telling Logano he was racing for points, "maybe [you need to] learn how to drive."
Logano accused Newman of not giving him room to pass and taking the air off the Stewart-Haas Racing car to ignite the accident.
"So you're not a good enough driver to pass me, is that what you're saying?" Newman asked.
Logano responded by saying the two race each other too hard every week.
"Dude, you're not giving me an inch," Logano said. "I was on the bottom and you doorjambed the [expletive] out of me."
Responded Newman, "I was six lanes up and I steered up and tried to miss you because you can't control your damn racecar."
Logano replied, "Cause I was [expletive] sideways because you were on my [expletive] door."
"He races everyone too hard," Logano said after the incident. "I'm not the only one that complains about it every week. And he just went in there and doorjambed me. I was down there trying to save it. When someone is right on your side it takes your air off. I'm down there hanging on and hanging on.
"I saved it three times before. I'm like, 'I can't save this one.' He should have given me more room by now."
David Newton covers NASCAR for ESPN.com. He can be reached at firstname.lastname@example.org.