Winner of the Hardwicke Stakes at Royal Ascot last June, Sir Michael Stoute's five-year-old will now attempt a repeat victory in the Group Two over a mile and a half.
For the first two days the place to be on the Knavesmire was the far side of the track, but after further overnight rain turned the ground rather dead, Moore was keen to grab the rail on the stands side.
It proved inspired, as there were challengers spread right across the track, including Ralph Beckett's St Leger winner Simple Verse, Hughie Morrison's Marmelo and the returning High Jinx, but Dartmouth came out best.
It was only narrow, with the 11-4 favourite beating Simple Verse by a neck with the same back to High Jinx, sent off at 40-1 having his first run for Tim Easterby on the back of a long lay off.
Last year's winner Clever Cookie was beaten two and a half lengths back in sixth, staying on strongly.
The Queen's racing advisor John Warren said: "I didn't think he was going to get there because they were so wide apart. Ryan had this plan to come this side, so he knew what he was doing, but I don't think he anticipated they were going to be so far away width wise as they were.
"It was hard to see from the stands whether he was going to get up. It was a remarkable ride, he's an absolute professional.
"I suspect Sir Michael will be looking at the Hardwicke again. That's his sort of race.
"He's an interesting horse because this (an extended mile and five furlongs) is as far as he's gone. It will be interesting to see how the remainder of the season unfolds after Ascot. We will have to look at the opportunities.
"Hopefully he goes to Ascot with a real big shout."
He went on: "The Gold Cup (at Ascot) would be a big ask. The thing is he would give his all and may leave his whole season behind.
"My view is that he's so good at what he's doing there's no need to find out.
"I'd say it will be the Hardwicke and then we might try and find out if he is a Cup horse.
"Dubai was the plan after Canada, where it went wrong, but he had a setback which meant he couldn't go which was a shame as it would have been nice to have a runner at the Carnival.
"We've always regarded him as nearly a Group One horse but abroad, sometimes that is enough to win a Group One."
Moore said: "He felt very easy the whole way, he's got mile-and-a-half pace, he was just doing a little too much in stages.
"He travelled beautifully and is such an honest horse, but it didn't help that I was apart from them and he's done very well.
"That's his fourth Group race now, we know what he is, he's a very honest horse."
Beckett said of Simple Verse: "It was a tremendous run, obviously the 3lb penalty didn't help but she will go to Ascot for the Gold Cup.
"I've no doubt she'll stay, she's a joy to train and she loves Ascot."
Easterby was thrilled with High Jinx, who was formerly with James Fanshawe, saying: "I'm delighted with that, he ran a cracker. He'll go to Ascot and then to France. It was his first run for us, his owners just decided on a change of scenery to freshen him up."
His rider David Allan was banned for four days (June 5-8) for using his whip above the permitted level
Marmelo was fifth for Morrison, who has been in the headlines this week as he fiercely protests his innocence having being charged by the British Horseracing Authoroity after one of his horses tested positive for nandrolone in January.
A report from the stewards following Marmelo's run said that an employee of the trainer had urinated in Marmelo's stable and having heard evidence from the veterinary officer, the equine welfare and integrity officer, the employee, and Morrison, they found the employee in breach of Improper Conduct under Rule (A)32.1 and cautioned him as to his future conduct in the racecourse stables.
"There's nothing to it really, the lad is a long-standing employee, he knows he's made a mistake and he won't do it again," said Morrison.
Morrison has offered a £10,000 cash reward for any information that can help prove his innocence in the case of Our Little Sister, who finished last of eight runners at Wolverhampton in an extended two-mile handicap.