Morneau had a two-run home run, Trevor Plouffe hit a solo shot two pitches later in the third inning and Moreau added a fifth-inning groundout to drive in another run for the Twins.
Walters (1-1) lasted 6 1/3 innings, walking three and striking out two along with the four hits allowed. All the Tigers' runs came on solo home runs off Walters.
Matt Capps pitched the ninth for his eighth save in Minnesota's 11 wins this season.
Detroit starter Doug Fister (0-2) gave up nine hits and four runs -- three earned -- in six innings.
Josh Willingham walked with two outs in the third inning and Morneau followed with his fifth home run of the season. Plouffe's third homer of the year made the score 3-0.
Willingham reached on an error by Detroit first baseman Prince Fielder and ended up on third to open the fifth. He scored on a Morneau grounder to second.
Brennan Boesch led off the bottom of the inning with his fifth home run of the season and Detroit's Andy Dirks opened the sixth with his fourth. One out later, Fielder connected for his sixth home run this year.