The 10-1 winner, ridden by Franny Norton, saw off favourite Benbatl in second with Crystal Ocean third.
Cracksman, who beat Permian in Epsom's Derby Trial in April, was ruled out of the York race by trainer John Gosden because of the rain-softened ground.
Permian is not entered for the Derby on 3 June but is set to be supplemented for the race at the cost of £85,000.
The Mark Johnston-trained horse is rated a 14-1 shot by bookmakers for the Epsom Classic, with Cracksman as low as 4-1 favourite alongside Cliffs Of Moher, trained by Aidan O'Brien.
Permian hit the front over a furlong out in the Dante, considered one of the leading Derby trials, and won by three-quarters of a length.
Benbatl could also line up for the Derby, but Crystal Ocean - whose odds for the Epsom race had been cut earlier in the week - is an unlikely runner, said trainer Sir Michael Stoute.
BBC horse racing correspondent Cornelius Lysaght:
What a thoroughly likeable performance by a thoroughly likeable horse who adds an interesting extra dimension to the Derby picture.
I loved the way in which jockey Franny Norton just had to administer the smallest amount of encouragement late on for his mount to respond quite convincingly.
Surprisingly, he'll be trainer Mark Johnston's first runner in the Epsom Classic in over 10 years.
Cracksman didn't run here and goes straight to Epsom, but his supporters will have derived satisfaction from the fact he beat Thursday's winner at Epsom in April.
Permian won the Dante Stakes at York and boosted the Derby credentials of non-runner Cracksman.