Jason Repko led off the Minnesota ninth with a double and scored four batters later when Kubel singled. Cuddyer followed with a run-scoring hit that handed the loss to Joaquin Benoit (0-1).
Matt Capps (4-3) got the final four outs, ending the Rays' rally in the eighth and allowing just a walk in the ninth for the win.
Minnesota took a 4-0 lead in the first, with Alexi Casilla, Joe Mauer and Delmon Young hitting consecutive doubles that made the score 2-0. Kubel knocked in a run and Cuddyer added back-to-back singles. Kubel then scored on a J.J. Hardy base hit.
Repko hit a home run in the fifth and Drew Butera doubled in another run in the sixth for the 6-0 Twins lead.