Pena's hit was sandwiched between RBI from Billy Butler and Chris Getz, giving the Royals a 4-0 lead against Rangers starter Colby Lewis (3-3), who hurt his own cause with a throwing error to open the floodgates.
Mike Moustakas socked a solo homer and Butler added a run-scoring double for Kansas City, which swept its two-game series at Arlington.
Vin Mazzaro (1-0) logged a victory in his first start of the season, holding the Rangers to three runs on seven hits over five innings.
Lewis lasted 5 2/3 frames, surrendering seven runs (two earned) on eight hits.
Brandon Snyder hit a solo homer for the American League West leaders, who lost for the third time in four games.