Trainer William Haggas later confirmed York's Juddmonte International will be the next target for Baaeed.
Japanese raider Bathrat Leon set a sensible pace in the mile showpiece, with Baaeed patiently ridden towards the back of the seven-strong field.
Cruising on the bridle, the 1/6 Baaeed was pulled wide by jockey Jim Crowley and immediately found another gear, powering clear with French Guineas winner Modern Games chasing him home.
July Cup winner Alcohol Free stayed on from the back of the pack to finish third.
"I'm relieved it's over. Baaeed is such a nice horse. It's great," said Haggas.
"Today was a big day. I can't tell you how sad it is for all of us that Sheikh Hamdan is not here to witness it. He did everything for days like this and he would have loved it.
"Baaeed has speed and class. I'm really looking forward to stepping up to 10 furlongs as I think he would enjoy it.
"I don't think we need to go for the Arc. I think we'll go for the Champion Stakes or the QEII depending on how he gets on at York."
"I just said to Jim in the paddock, we've got him for two more races after this so let's just enjoy him and make the most of him, because he will most likely go to stud at the end of the year and I'll spend the rest of my training career trying to find the next one.
"If Baaeed can win five Group Ones trained by us then he must be (very good)! He is a very straightforward horse."
Comparisons with Frankel - who went to York after his second win in the Sussex before signing off at Ascot in the Champion Stakes - continue to be inevitable, and Crowley is in no doubt about his mount's class.
He said: "He's got everything, a turn of foot. You can put him anywhere in a race. You can make the running, you can drop him out. Good horses like that, they just tick all the boxes. It will be interesting up to a mile and a quarter next time - I'm looking forward to it.
"If he can show that turn of foot over a mile and a quarter - he switches off and relaxes, he could well be (the greatest).