Moehler (4-4) evened his record despite giving up three home runs, including a leadoff shot by Brendan Harris.
Joe Mauer hit his career-high 14th homer and Delmon Young also connected for Minnesota.
Twins starter Scott Baker took a 3-1 lead into the seventh. But Hunter Pence keyed a four-run rally with a one-out double and Ivan Rodriguez chased Baker with an RBI single.
Jason Michaels followed with a run-scoring double off reliever Sean Henn (0-3) and Bourn put the Astros ahead to stay with his second homer of the season.
Berkman’s solo shot off Luis Ayala in the eighth made it 6-3. Jason Kubel pulled Minnesota to 6-5 in the eighth with a two-run homer off reliever LaTroy Hawkins.
