"The joy and relief are naturally huge," said Bremen's team manager Klaus Allofs, just a week after having lost UEFA Cup final to Shakhtar Donetsk in Istanbul.
"We have had some difficult weeks, which makes the win ever more enjoyable. We had three players who weren't available in the UEFA Cup final in Diego, defender Per Mertesacker and striker Hugo Almeida and they made the difference here."
Brazilian midfielder Diego, in his last appearance in Germany before his move to Juventus, signed off by creating the winning goal for Özil after 58 minutes.
The 24-year-old Diego, who has signed a five-year deal worth €24.5 million to move to Italy, beat three defenders and slid a pass into the path of Özil who fired home past Leverkusen goalkeeper Rene Adler to give Bremen the winner.
Leverkusen had their chance to equalise when, with just four minutes of normal time remaining, Germany striker Stefan Kiessling fired wide for Bayer as their attack failed to beat Bremen goalkeeper Tim Wiese.
Both Bremen and Leverkusen under-achieved last season, finishing mid-table in the Bundesliga, and Bremen's Germany midfielder Torsten Frings said winning the German Cup title for the sixth time in the club's history was satisfying.
"We put in a good performance and deserved the win," said Frings. "The Bundesliga season was not satisfying, but we have been in two finals and won a title, which puts us in the Europa Cup, so we have to be content."
Bremen's sixth German Cup title means only German giants Bayern Munich have won the cup more having lifted the trophy on 14 occasions.