Pizarro found the net from a corner by substitute Ze Roberto in
the 59th minute and it was enough to earn Felix Magath's team their 13th German Cup crown.
Bayern clinched the double last season with a 2-1 cup final
victory over Schalke 04 and a second successive league title is on the cards with just five points needed from the remaining three games to defend their Bundesliga crown.
Eintracht at least had the consolation of qualifying for next
season's second-tier European competition, the UEFA Cup.