Cespedes put the A's ahead to stay with a first-inning single and then hit the second of three Oakland homers in the second.
Jonny Gomes (3-for-4, three runs scored) delivered a two-run shot and Chris Carter added a bases-empty clout during the big frame. Seth Smith chipped in a sixth-inning solo blast as Oakland outscored Minnesota 24-10 in the series.
Oakland belted four homers in back-to-back games for the first time since 2001 and won for the ninth time in 10 contests overall.
Jarrod Parker (6-4) corralled the victory, yielding four runs on nine hits over six innings. The A's right-hander didn't allow a walk and struck out four.
Twins starter Brian Duensing (1-6) lasted only two innings, surrendering six runs on seven hits.
Ryan Doumit and Brian Dozier each supplied two hits and an RBI for Minnesota.