Dovizioso's qualifying time of one minute 45.256 seconds was more than half a second quicker than Rossi's best.
Rossi, 37, won at Assen last year and is also chasing his second successive victory after his triumph in Barcelona earlier this month.
Britain's Scott Redding secured his first front row start with third place on a non-factory Ducati.
Honda's Championship leader Marc Marquez will start fourth with defending champion and fellow Spaniard Jorge Lorenzo, who crashed in third practice, a disappointing 10th on his Yamaha.
"It was a heavy crash even though it was a small crash," Lorenzo said of his fall. "The gravel was very close to the track and when I arrived to it I had a very high speed and I rolled through the gravel a lot.
"A lot of rocks hit me in the neck, on my back and my hip, so I damaged my skin and superficially have a lot of pain, but luckily not in my bones, they are OK so I can race without any problem.
"I don't think it had an effect on qualifying, I just didn't feel safe or comfortable in the rain on wet tyres."
Dovizioso's team mate Andrea Iannone starts last after being sent to the back of the grid by stewards for causing a collision with Lorenzo in Barcelona.
Spaniard Maverick Vinales crashed his Suzuki early on in the session, with Marquez also coming off at turn eight.
(Reporting by Alan Baldwin, editing by Martyn Herman)
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