He had moved from Chelsea a couple of seasons earlier and had quickly become a firm favourite in east London.
Now 67, Brabrook still vividly remembers that day as he looks out across the club's training ground at Chadwell Heath, where Pardew and his players are preparing assiduously for another momentous challenge against Preston.
"It's strange how this year has worked out," said Brabrook, who still works for the club on a part-time basis.
"First Chelsea won the title for the first time since 1955 and it was that year, as a 17-year-old, that I began breaking into their first team.
"Now West Ham are in a major final against Preston, a repeat of that 1964 Cup Final. It's a long time ago now but I remember that day as if it were yesterday. I remember the build-up to the game. We had two weeks to think about it then after the end of the league season, the night before in a hotel and then on to Wembley for the final.
"I can also recall the match so clearly. We were big odds- on favourites that day but Preston played better than us, in the first half especially. Twice we went behind and twice we pulled level.
"I can remember the clock ticking down and both teams straining for the winner. It looked like it was going into extra time."
It was at this point, with less than three minutes left, that Hurst galloped one more time across the Wembley turf before releasing the ball to Brabrook on the right.
"I had nothing left, nothing at all," he recalled. "The Wembley pitch was notorious for inducing cramp in those days and both my calves had seized up. They were like concrete.
"My socks were down around my ankles but I managed to push the ball in front of me and look up. There, in the middle, I saw Ronnie Boyce making a run into the box and unmarked.
"I managed to get a good contact and Boycey did the rest, heading home the winner."
Brabrook hopes that history will be repeated next Monday but believes the match could be just as close.
"I hope to be in Cardiff for the game," he said. "I think it will be a much tougher match than against Ipswich but I am confident we'll do it this time. We need to be back up there with the best clubs in the land."