The sluggish start to United's title defense has seen new manager David Moyes collect just seven points from a possible 18 to languish six points behind provisional leader Tottenham.
Although Wayne Rooney canceled out Morgan Amalfitano's stylish solo goal, Saido Berahino clinched a 2-1 victory for West Brom at Old Trafford.
Last weekend City had been toasting derby glory over United, but was brought down to earth by a 3-2 loss at Villa.
City twice threw away the lead before Andreas Weimann struck Villa's winner to leave the visitors without an away win this season.
City is just three points behind Tottenham, which was held to a 1-1 draw by Chelsea.
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