Callaspo's rap staked the Royals to a 4-1 lead that held up as Oakland scored single runs in the seventh and eighth inning.
Jay Marshall (0-2) took the loss after starting the sixth in relief of starter Edgar Martinez.
Closer Joakim Soria pitched the final two innings for his 21st save.
Kyle Davies (6-9) went six innings for the win. He gave up one run on four hits and struck out six.
Rajai Davis hit his third home run of the season off Davies in the first inning. Adam Kennedy and Mark Ellis drove in the other Oakland runs.
Callaspo also scored a run for the Royals on an RBI by Miguel Olivo.
Copyright 2009 by United Press International.