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.
Source: Autosport