Almagro had been seeded 13th for the event however he was brushed aside by the Bulgarian - with Dimitrov claiming a 7-6 (7-3) 6-4 win.
It was a bad day for the seeds with Fabio Fognini and Jerzy Janowicz joining Almagro in bowing out.
Fognini, ranked 14, slumped to a 6-2 6-4 loss against Radek Stepanek, while 16th seed Janowicz was ousted 6-1 7-5 by James Blake.
Blake's win was one of the few bright moments for the home fans, with Mardy Fish, Sam Querrey and Mackenzie McDonald all failing to progress.
Fish suffered a 7-5 6-2 defeat to Philipp Kohlschreiber and wild card McDonald was blown away 6-1 6-1 by David Goffin.
Querrey showed some fight in his encounter with Janko Tipsarevic, however he eventually lost 6-7 (5-7) 6-3 6-4.
Brian Baker did overcome Denis Istomin 7-5 6-3, though, to join Juan Monaco, Jeremy Chardy, Marcel Granollers and Dmitry Tursunov in reaching the second round.