The German side went into the clash at Anoeta needing to better Shakhtar Donetsk's result at Manchester United, and the English champions lent Leverkusen a hand.
United defeated Shakhtar 1-0, while Omer Toprak's second-half strike ensured Leverkusen defeated Sociedad to claim second place in Group A.
Hyypia shared insight as to what he said at the interval with both games locked at 0-0, which involved an accurate prediction.
He said: "I told my players at half-time that we would score a goal from a set-piece today and that we only have to believe in ourselves.
"When I heard that Manchester were 1-0 up in their game, I knew that we didn’t have to risk more than was necessary."
Club captain Simon Rolfes labelled Leverkusen's progression as "very important" but rued missed chances at Sociedad.
He added: "It's very important for us to know that we will play in the Champions League next year. We should have scored a lot more goals.
"We controlled the game in the first half and in the second we applied more pressure. It was a deserved victory."
