Favourite Air Force Blue, winner of the Dewhurst Stakes last year and four of his five races, never challenged and was a distant 12th of the 13 runners.
Dettori crossed to the rail side to win by one and half lengths for his third victory in the prestigious mile race.
Massat (9-1) was second with Ribchester (33-1) two lengths back in third.
Air Force Blue was widely expected to give trainer Aidan O'Brien a record eighth 2000 Guineas success.
But Ryan Moore could find no response from the bay colt and it was Dettori who surged clear, 20 years on from his first success in the race on Mark of Esteem.
He also won again in 1999 on Island Sands.
The veteran jockey, 45, said of his latest triumph: "We had a bad draw but he's a great horse.
"His main forte is that he stays, he galloped out really strong."
Trainer Hugo Palmer said: "Frankie was so alert, he said nothing had been coming from behind and that if nothing took us on, he would do it himself and he did.
"There were no hard luck stories, for us anyway. It was a masterful ride."
BBC horse racing correspondent Cornelius Lysaght
"Considering the going was on the soft side, the time was decent so that's another plus about a success achieved by a decisive length and a half.
"The winner had to race on the more challenging outside of the field because he was drawn in stall one, and Frankie Dettori gave him extra credit for the performance because of that.
"This was Hugo Palmer's first British Classic win; he's very much an emerging force - it won't be his last."
Frankie Dettori rode 14-1 shot Galileo Gold to a surprise victory in the first classic of the 2016 Flat season, the 2000 Guineas at Newmarket.