The Englishman rattled in a string of pressure putts to earn a vital point from his fourballs match on the Saturday afternoon, when he was paired with Rory McIlroy against Jason Dufner and Zach Johnson.
At that time, Europe trailed the US by 10-5 with only that match left on course.
Poulter then overcame the in-form US Open champion Webb Simpson in his singles match on Sunday to edge his team on their way to an historic victory.
Olazabal, who was a close friend of Ballesteros, said that Poulter's performance reminded him of the great man.
"For whatever reason this event for [Poulter] means so much," said the Spaniard. "He thrives in it and I think it brings the best of him on the golf course.
"That is why he managed to do what he did on the Saturday afternoon, it was just amazing. In a way he reminds me a bit of Seve in that regard, that intensity, that focus, that will to win the point is very close to Seve."