Five other top stayers, including Further Flight and Persian Punch, had won the race twice - and Stradivarius showed the fire still burns bright with a battling performance under his regular pilot Frankie Dettori.
Spanish Mission and William Buick made the John and Thady Gosden-trained seven-year-old fight all the way and was narrowly in front at one stage, only for Stradivarius to find that little bit extra in the dying strides to win by a head.
The paid had the Group Two stamina test to themselves after The Grand Visir had taken the four-runners into the long straight.
Stradivarius (4/6 favourite) knuckled down when it looked as though Spanish Mission might lower his colours to record his 18th victory.
Dettori and Stradivarius paraded in front of the packed stands and were given a tremendous reception all the way back to the winner's enclosure, where the jockey gave his trademark flying dismount.
The Italian said: "When we went across the line and they announced the result there was a big roar from the crowd, an explosion.
"I love the horse so much. He's not getting any younger, it was always going to be a messy race and I was using Richard (Kingscote on The Grand Visir) as a reference point, but when William came I had to go straight for home.
"He only does enough when he hits the front and William wouldn't go away! He passed me, I passed him back then he passed me again - but I think he knows where the line is as he popped his head out just in time!
"My heart lost a few beats, I'll be honest, but it was a tremendous horse race and the reception he got was special."
He went on: "I didn't want to kick too early, but I didn't want to get jumped on either. Strad is a horse who likes a target and unfortunately we didn't have it, so I pushed Strad close to William to make him race.
"Every time he's run here I think he's run below par. I feel he's much better at Ascot, but we got the job done so I won't criticise him.
"John, Rab (Havlin) - the whole team have done a great job with him, he's a joy to have as he's such a character. I'm feeling emotional."
Gosden senior said: "It was always going to be a fascinating race, Spanish Mission put it up to him and Frankie said he was headed, then he got back and then he was headed again and he got back - it was a proper race for everyone to watch.
"He's phenomenal, to have won four Goodwood Cups, three Gold Cups, three Lonsdales now, three Yorkshire Cups, a Doncaster Cup - all those miles of racing, never mind miles of training.
"Full marks to him, a great performance and we'll see what we want to do next.
"He still enjoys his training, he's very enthusiastic, a stronger-run race at his age, so he can come at them, probably suits him better.
"The horse will tell us, it's not our decision, as long as he's enjoying his racing and training and he's very enthusiastic, which he is and he's a very happy horse, he has a very good sense of humour as well - as long as you've got all of that then fine, we keep racing.
"The moment that seems to be fading that's when we stop."
Reflecting on the finish, he added: "I was just waiting for the photo finish, I've got it wrong before so I've learned to just wait.
"His enthusiasm is perfect, he won the Sagaro and if Frankie could ride the Ascot Gold Cup again he'd ride it differently, he sat too far back and he got in trouble.
"I'm not saying for one moment he'd beat the winner (Subjectivist), but my God he'd have given him a good race.
"He loves Goodwood, he loves the twists, but then there was 60 millimetres of rain the night before so that, to me, was the biggest disappointment.
"He was headed, he came back, he was headed again and he came back - that to me shows a lot of willingness.
"He's not a horse you train, I let him train himself. If you get a great player, a great footballer and they come to your club, if you start thinking when they're 30 or 32 that you're going to start drilling them, they'll tell you what to do with your management.
"It's the same, you play with him and let him train the way he wants to."
On immediate plans, Gosden said: "The Doncaster Cup is a possibility and there is Champions Day, I hope it's decent ground but if it's bottomless we might have to reroute."
Anna Lisa Balding, assistant trainer to her husband Andrew, was proud of the runner-up.
She said: "He's run a hell of a race and I actually thought we'd won when he went ahead. I thought we'd got him, but we didn't.
"Someone just said to me to have a good race you need two good horses and he had it everywhere bar the line.
"We'll stick to Plan A, Australia here we come (for the Melbourne Cup) and let's hope he does his stuff out there.
"It will mean two weeks in a hotel probably so I'm not sure who'll be putting their hand up for that trip!"