Just after the halfway mark, on lap 36, de Vries made a bold overtake into Turn 1 while the pair were squabbling over 12th place.
Magnussen refused to yield on the outside, which became the inside for Turn 2, and the pair then traded glancing blows, which allowed Mercedes' George Russell past.
De Vries and Magnussen continued their fight towards Turn 3, where de Vries outbraked himself on the bumpy inside line and forced both cars into the run-off area, losing any hope of a points finish for either driver.
The stewards deemed their tangle a racing incident, which both drivers were satisfied with.
"He was racing pretty hard, that's for sure. But who am I to complain about that?" said Magnussen, who has a reputation for being aggressive himself.
"I think the problem was he missed his braking in Turn 3 and took me with him. That was it.
"He had the inside but then outbraked himself and couldn't make the corner.
"I was on the outside, so I was blocked, and we ended up on the run-off with him. That was unlucky for me."
De Vries explained the bumpy nature of the inside line into Turn 3 caught him out as he locked up the front-left tyre.
"We were just racing each other hard through [Turns] 1, 2," he said. "I was kind of on the dirt, pushing each other hard into that braking point, and I locked up and went straight.
"There was less grip and it was very bumpy, which didn't help. It's also not really a straight braking zone, you're constantly turning a bit, which is tricky."
The Dutchman equally didn't blame Magnussen for his aggressive defence into Turn 1, which led to the initial contact.
"I felt like I had the momentum and thought I kind of had him, but then he almost went for the grass, on the kerb to get me back," said de Vries.
"But I don't blame him, that's part of the game. It was a racing incident, nothing more or less."
Additional reporting by Adam Cooper
