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United saw much of the ball in the opening 15 minutes, but could not fashion any chances with their superior possession.
Their lack of creativity came back to haunt them in the 18th minute as Benteke bent a measured shot inside the far post from inside the box, after Jonny Evans was unable to deal with a deep free kick.
United were soon on the front foot again as they penned the hosts back inside their own half, but a wall of claret and blue shirts prevented them from carving open any opportunities.
After a Villa counter-attack broke down, United almost got a goal back as Ashley Young's inswinging cross evaded everyone inside the box, but Brad Guzan clawed it away just as it looked to be creeping inside the far post.
Radamel Falcao was close to connecting with a couple of dangerous Antonio Valencia crosses as half time approached, but a mass of bodies prevented the Colombian from getting a shot at goal on either occasion.