Max Dynamite ($20), runner-up in the 2015 Cup for another Irishman Willie Mullins, was another 2 lengths third.
"He is not a big horse, 420 kilos, but he is an easy horse to train," O'Brien said.
"I'm almost speechless. He was brilliant and an unbelievable ride by Corey."
Brown, who won his first Cup on Shocking in 2009, said the race had not begun as he envisioned but panned out how he hoped.
"I was concerned in the first furlong because there was more early speed than I thought there would be," he said. "There was a bit of confusion in front of me so I just let the horse relax and get into his rhythm.
"He was always travelling and I felt he was the winner a furlong out.
"I've won this race before but this time it feels a bit surreal."
Williams, who has won three of the past six Melbourne Cups with European imports Green Moon (2012), Almandin (2016) and Rekindling, said his latest winner would return to Europe for the Gold Cup at Royal Ascot which he won in 2016 with Order Of St George.
There was plenty of drama just hours out from the race, as Ben Allen replaced Joao Moreira aboard Thomas Hobson for Willie Mullins - after Moreira suffered a nasty fall in race four on the card.
What the jockeys said
Corey Brown (Rekindling) 1st: "I've been back from overseas for about nine months, slowly but surely getting back to where I was, but I can't believe it. Honestly it's so special, I've got my family down here with me, the girls, they're old enough to come to the races now and enjoy it. I'm lost for words, I can't believe I did it again."
Ben Melham (Johannes Vermeer) 2nd: "We had a great run throughout. I was spending my money at the furlong, I thought we were home, but just the weight was the difference."
Zac Purton (Max Dynamite) 3rd: "An excellent run. He was very brave. He took a tight run when I asked him to and when I got through there, I thought we were in for the fight but he's a bit old now ... but he was terrific."
Brenton Avdulla (Big Duke) 4th: "He was awesome. We had a perfect run and I was following Corey (Brown) through and I thought I was half a chance, the nerves started to kick up a bit ... a bit of excitement on the corner but he ran out of gas in the straight."
Glyn Schofield (Nakeeta) 5th: "Super run. He just kept coming strongly."
Ben Allen (Thomas Hobson) 6th: "He just didn't pick up the bridle at all early. I thought he ran really well."
Olivier Peslier (Tiberian) 7th: "In the straight he was coming well but in the last 200 (metres) he was immediately beaten."
Dwayne Dunn (Libran) 8th: "He ran really well ... as good as he could run."
Hugh Bowman (Marmelo) 9th: "I expected a bit more. I had to make a little bit of use of him early but I was in a nice position throughout and he relaxed well. The pressure built a little earlier than I would have liked but I thought he would have taken me a bit further."
Stephen Baster (Wicklow Brave) 10th: "He ran well. He just didn't have any early speed at all so he got back last and he didn't get going until the 650 (metres) but he ran home good."
Kerrin McEvoy (Red Cardinal) 11th: "We made nice progression round the corner then I got into the clear and he just probably felt the ground the last furlong and a half."
Frankie Dettori (Almandin) 12th: "I was stuck three-wide but the horse was flat. He never carried me today and ran like a flat horse."
Beau Mertens (Cismontane) 13th: "Happy with the performance ... a lot of good horses finished in front of him but he did the best he could."
Dean Yendall (Amelie's Star) 14th: "I thought there'd be a more genuine tempo. I got stuck out a bit and I would have liked to have had a bit more cover. "
Cory Parish (Boom Time) 15th: "It was probably just too slow a tempo for him. He's probably better suited at a mile and a half."
Craig Williams (Wall Of Fire) 16th: "It was a bit of a muddling stop-start race and I thought my horse responded really well under those conditions. He came off the bridle at the 700 which is normally to his liking ... but he didn't stay on at all today. He just didn't run up to his European form."
Kathy O'Hara (Single Gaze) 17th: "She got knocked around a lot in the race and never had a lot of luck in running. She was brave enough to run on past a couple late but it was just too rough for her."
Jamie Spencer (US Army Ranger) 18th: "He passed a few beaten ones but I never thought he'd win."
Blake Shinn (Humidor) 19th: "He just doesn't run two miles. I gave him a nice run throughout but the pressure went on and he just didn't respond."
Damian Lane (Hartnell) 20th: "He didn't see it out today. He settled in a lovely rhythm and at the 400 (metres) I knew he wasn't going to run (the distance) out."
Glen Boss (Ventura Storm) 21st: "Had a good run in the race but I expect he got his tongue over the bit at some stage in the race and he choked down and didn't run it out."
Michael Walker (Bondi Beach) 22nd: "I don't think his mind really wants to be there at the moment. He tried to run through the fence for the first 50 metres of the race."
Michael Dee (Gallante) 23rd: "He was very disappointing. The track was obviously a little bit too dry for him but I didn't expect him to go that badly."
- AAP
