Ventura did strike out six batters, but suffered his first loss of the season.
Minnesota (9-9) pounced on the 22-year-old in the first inning as Trevor Plouffe plated two with a double to deep right. The Twins score the first five runs of the game while sending Ventura off early. Minnesota slapped 13 total hits.
Omar Infante and Alcides Escobar drove in Kansas City's runs, Escobar's coming on his first home run of the season in the seventh.
Justin Marks made his major league debut in relief, striking out Joe Mauer as the first batter he faced before allowing three runs on four hits. He struck out two total Twins.
Phil Hughes (1-1) gave up nine of the Royals' 11 total hits, but held them to three runs over six innings while striking out three.
Kansas City (9-8) is on the road for the next seven games, beginning Monday with a four-game series in Cleveland.