The Saeed bin Suroor-trained colt was landing his third Group One event in a row and dug very deep to just prevail from Homesman in the tightest of photo finishes.
Given a superb ride by Pat Cosgrave, the Godolphin-owned runner found things against him from the start, missing the break from his wide draw, but was coolly manoeuvred into a good position.
Kicking rounding the turn with two furlongs to run, Cosgrave’s mount answered every call as the challengers loomed large, and got the verdict by a short head.
The Cliffsofmoher (Cliffs Of Moher) was third for Aidan O’Brien, with the Andrew Balding-trained Duretto fourth.
Bin Suroor, who teamed up with Cosgrave to win the Ladbrokes Stakes with Benbatl last weekend, told Racing.com: “It was Sheikh Mohammed’s decision to send him to Australia after he won two Group Ones in Germany and it is a brilliant result for him.
“The horse is doing good and the Melbourne Cup is a big race, it’s another dream for us, but we will try.”
Cosgrave said: "I've got to give all credit to the horse.
"I had a bad draw, jumped slowly and had to commit earlier than I should have. He was there to be beaten, but he's so tough and genuine.
"I think anything is possible after today."
He added: "It’s been a wonderful week. It wasn’t an ideal start and he was slow away, but I ended up getting a good position halfway down the back straight.
“It was quick early for the first 400 metres, then they dawdled down to the 600 and that’s why I kicked early – my horse is a good stayer.
“He’s been a wonderful horse for me over the last 18 months and hopefully we can go on to Melbourne now.”
Bin Suroor now has two Caulfield Cups following the success ten years ago of All The Good.
The trainer, who has won eight Group 1s across the world this year, paid tribute to His Highness Sheikh Mohammed for targeting the Caulfield Cup with Best Solution.
"It was his decision to send this horse to Australia, and it's great to see Best Solution win the Caulfield Cup after winning two Group 1 races in Germany earlier this year," he said.
Bin Suroor has finished runner-up in the Melbourne Cup three times, and confirmed Best Solution would be bidding to end the drought on November 6.
"The Melbourne Cup is a very big race for us. It would be a dream to win it," he added.