A Prince of Arran finished third.
The Melbourne Cup has been marred by the death of star United Kingdom galloper The CliffsofMoher.
Described as a "tragedy" by veteran Seven commentator Bruce McAvaney, the United Kingdom raider pulled up lame as the field passed the finishing post for the first time.
"And (wife) Cathy and myself have been looking around for a bigger house. and I said to one of the reporters yesterday that if I won I would buy Cathy a new house, so look out", said McEvoy.
"At 400, I had to go my own way and I was full of running".
"It's such a huge thrill to win this for Sheikh Mohammed, to repay the faith that he showed in me", McEvoy said.More news: Rose back on top of the world
Appleby admitted on Tuesday that winning the race for the Dubai outfit ticked off a box on his bucket list, but while the English trainer was able to bask in the glory of victory, he was later also quick to praise his boss and the team.
"Today's tragedy is a stark reminder of the risks these horses face every time they run, and highlights that behind the gloss and glamour of Cup celebrations there is a dark reality", said Speechley. "It's not sunk in yet".
Cross Counter is also a member of a family with which Sheikh Mohammed has been involved through four generations.
"He's the one that's given us the encouragement to take the chances in what we do".
"The horse himself, we were confident coming in, we had the right horse".
"With Kerrin McEvoy in the saddle I just gave him a blank page and said "ride it as you find it".
"I always thought he was the horse to worry about".More news: All Blacks still have faith in Williams ahead of England clash
Favorite Yucatan, prepared by O'Brien, finished 11th, with the Irishman's other entrant Rostropovich fifth in a disappointing race for the master trainer.
But the weather cleared after midday, buoying a festive crowd and drying out the track from heavy to soft an hour before the race.
Marmelo claimed the lead inside the final furlong of the $7.3 million race but was grabbed late by the fast-finishing Cross Counter who won by a length, with a further two lengths to A Prince Of Arran in third.
But he bolted home with energy to spare as a grinning McEvoy rose from his saddle.
Godolphin's other horses were the James Cummings-trained Avilius, who finished 23rd, and Caulfield Cup victor Best Solution, who came eighth.
Japan-based Chestnut Coat, trained by Yoshito Yahagi, was 14th.More news: Real Madrid fullback Dani Carvajal: Lopetegui best coach I've had
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