The Americans lost 2-1 to Germany when Blake and Meghann Shaughnessy fell to Nicolas Kiefer and Sabine Lisicki 6-3, 3-6 and 10-7 in the tiebreaker.
Blake defeated Kiefer 7-6 (3), 6-7 (7), 6-4 to set up the deciding match after Shaughnessy lost to Lisicki 4-6, 6-0, 6-4.
After losing 3-0 to Slovakia in the opening match, the U.S. team needed to beat Germany and Australia to have a chance of reaching Friday's final in the international mixed team tournament.
The winner of the Germany-Slovakia match will top Group A and advance to the final. The United States will end the round-robin against host Australia.
Blake won back-to-back Hopman Cup titles with Serena Williams and Lindsay Davenport in 2003 and 2004.
The Russian brother-sister combination of Marat Safin and Dinara Safina top Group B after defeating Taiwan in singles matches. Safina stopped Hsieh Su-wei 4-6, 6-2, 7-5, while Safin won 7-6 (6), 7-5 against Lu Yen-hsun.
Russia will play France on Thursday.
Guardiola Pleased Yet Sad With Barcelona Defeat
Blake wins, forcing U.S-Germany to doubles
