Isner returned to Court 18, which now boasts a plaque to commemorate last year's record-shattering 11-hour epic win against Nicolas Mahut, but was beaten 7-6 7-6 6-7 6-3.
Isner had beaten Mahut in a much-hyped rematch in the first round but was never able to make much impression against the hard-hitting 16th seed Almagro.
He served 28 aces but did not have a single break point on the Spaniard's serve. Almagro claimed the only break of the match early in the fourth set as he went on to seal a third round encounter with Russian Mikhail Youzhny.
(Reporting by Martyn Herman, editing by Mark Meadows)