The unbeaten colt justified 7-4 favouritism by storming clear on the rails in the big race of the year for two-year-olds.
A week ago, Channon's former colleague Kevin Keegan was walking out of the England job.
But Channon was walking into the winner's enclosure on Saturday after one of the best results of his relatively short career as a racehorse trainer.
Australian jockey Craig Williams had a cosy ride on the winner, seeing off the challenge of Frankie Dettori on Noverre in second.
Sir Michael Stoute's 40-1 outsider Tempest completed the placings in the 7f contest.
After the win, Channon paid tribute to his star, who will now be well fancied for next year's Sagitta 2000 Guineas
"We've always known he was a good horse. He's got speed and you can ride him from behind or in front," he said.
But the victory of Channon's youngster, gaining his second Group one win following the Prix de la Salamandre four weeks earlier, left a major talking point.
Would Tobougg, owned by Sheikh Ahmed Al Maktoum, be recruited to the ranks of Godolphin?
Channon fended off inquiries and said: "Don't ask me. I just train them. I don't worry about where they finish up."
Tobougg is generally second favourite for the Guineas, being as low as 6-1 with William Hill. Nayef heads the market on 9-2.
Sent off 7-4 favourite for the Dewhurst, Tobougg was always handily placed and having led approaching the final furlong was kept up to his work by Craig Williams to score by one and a quarter lengths from Noverre.
Channon admitted to feeling the pressure. He said: "It's a big relief. Races like this are our cup finals and that is where you want to be.
"That's what it's about. When you've got a good one you want them to produce on the track what they invariably do at home. Just happens I've got a pretty exceptional horse."
Williams, due to return shortly to Australia, was gaining his first success at the highest level in Britain.
He said: "He got to the front and had a good look at the crowd. He was just enjoying the moment."
Runner-up Noverre could run next in the Breeders' Cup Juvenile at Churchill Downs next month.
Darley Dewhurst Stakes, Newmarket,
1530 BST
1 Tobboug 7-4f, 2 Noverre 7-1,
3 Tempest 40-1. 10 ran.