Texas starter Yu Darvish took a no-hitter into the seventh with the Rangers holding a 2-0 lead.
Darvish, however, walked Brian Dozier to open the seventh and then gave up the homer to Hermann on a 2-0 pitch that ruined his no-hit bid and tied the contest. Morneau followed with his 17th home run of the season.
Darvish, who struck out 11, slipped to 12-6 despite flirting with a no-hitter for the third time this year. He retired the first 26 men he faced in his first outing of the season against Houston before losing the potential perfect game.
Minnesota's comeback gave the win to starter Liam Hendricks (1-2). It was only the second victory in his 25 starts scattered over three major-league seasons. He gave up one earned run on five hits in six innings.
Glen Perkins struck out two in the ninth on the way to his 31st save.