There were five touchdown plays of 58 yards or more and the teams combined for 914 yards of offense -- 562 of them produced by the Vikings.
Posey's touchdown catch gave Houston a 14-3 lead and the Texans stayed in front thanks in part to a 76-yard punt return early in the third quarter by Trindon Holliday.
After a second-period field goal, Minnesota scored on a 58-yard pass from Sage Rosenfels to Devin Aromashodu, a 59-yard throw from McLeod Bethel-Thompson to Jarius Wright and a 76-yard run by Jordan Todman.
Houston's Justin Forsett ran for 114 yards and two touchdowns while Beck completed 6-of-10 for 149 yards.
Bethel-Thompson had 193 passing yards and Rosenfels added 111.
Houston (3-1 in exhibition play) will open its season at home against Miami. Minnesota (1-3) will host Jacksonville in its opener.