Both hit two-run singles in the bottom of the fifth inning when Minnesota scored all of its runs. Justin Morneau added a sacrifice fly.
Cassilla's hit, which gave the winners a 4-3 lead, was the eventual game-winner. He and Buscher had two hits for the Twins, who swept the three-game inter-league series at the Metrodome.
Winner Livan Hernandez (8-4) gave up three runs -- one earned -- on nine hits and a walk in seven innings with five strikeouts.
Closer Joe Nathan recorded his 19th save.
Arizona got two hits and one RBI from Chris Snyder.
One run scored on Delmon Young's fourth-inning fielding error and another scored on Hernandez's wild pitch, also in the fourth.
The Diamondbacks' Conor Jackson had three hits, and both Snyder and Mark Reynolds had two hits.
The losing pitcher was starter Brandon Webb (11-4).