The Brewers committed four errors while losing their third straight.
It was a 2-2 game through four, but Minnesota scored nine times over the next four innings to turn the game into a rout.
Span went 4-for-5 from the lead-off spot and scored three times to rev up Minnesota's 16-hit attack. Mauer drove in two runs in the fifth with a double and had another RBI double during the Twins' four-run eighth. Morneau had a sacrifice fly in the seventh and singled home two runs in the eighth.
Josh Willingham opened the Minnesota scoring in the first with a two-run homer.
Scott Diamond (3-0) lasted 5 1/3 innings to get the win. He gave up three runs on eight hits. Marco Estrada (0-3) surrendered four earned runs on six hits in five innings. In a five-year career, Estrada has just four victories, all of them coming last season.