Olazabal's side trailed 10-4 at one point on Saturday afternoon and were still four points down going into Sunday's singles, exactly the same margin from which the home side won in controversial circumstances at Brookline in 1999.
But after being on the receiving end of last-day heroics 13 years ago, Olazabal was able to enjoy the "Miracle at Medinah" as eight of his team won their singles matches and Francesco Molinari's half point against Tiger Woods completed a remarkable win by 14.5 points to 13.5.
"This has been a very special week," said Olazabal, whose team were dressed in the colours of the late Ballesteros and had a silhouette of the former Ryder Cup captain on their bags all week.
"Seve, it's the first time that he's not here with us at the Ryder Cup. I do have wonderful memories from my matches with him. He was a very special man and he's very close to my heart.
"All these guys sitting here in this media room know how much this week has meant to me. I get emotional about it but I want to thank them for what they did today. They gave me the best week of my life.
"And I'm just glad that I had the 12 men on my side ready to give their best during the whole week.
"The start of the week was a tough one. Nothing went our way, but these guys kept on believing, and I'm sure that not just the silhouette, but the phone call Seve made last time at Celtic Manor in 2010 and all the images of Seve around the clubhouse, the locker room and things like that, kept that spirit alive.
"So it's not just me. I think these guys did it also for him."
Ian Poulter was the star of the show for Europe, winning all four of his matches in his trademark passionate style to more than justify his selection as one of Olazabal's two wild cards.
"We have actually revised the qualification for next time," Lee Westwood joked. "It's nine (qualifying) spots, two picks and Poults. It's the Poults clause."
Poulter, who now has an amazing record of 12 wins from 15 Ryder Cup matches, added: "I'm officially taking two years off and I'll see you at the next one."
Asked to explain his success in the contest, the 36-year-old said: "I don't know. It's a passion I have; it's a passion I've seen at the Ryder Cup for years and years as a kid growing up, and it's something that comes from within.
"I just love it. I love the whole fact that I've got 11 great team-mates, a fantastic captain and vice captains, and I love the team atmosphere. It's something very, very special to be a part of.
"It's been a truly inspirational day. It's been history in the making."