The Twins built a 5-0 lead through two innings and easily survived despite a rough start for Kevin Slowey.
Slowey (3-2) had his start moved up due to a medical emergency in the family of scheduled starter Nick Blackburn. Slowey gave up nine hits but limited Cleveland to three runs over five innings.
The Twins were coming off their first lost series of the season. Cleveland has dropped four out of five.
Carmona (3-1) gave up six runs on eight hits in six innings to suffer the setback.
Minnesota finished the month with a 15-8 record, its first winning April in three years.