City looked in control and cruising for much of the first half and took the lead when Dias swept home a lovely, left-footed strike from outside the area.
We were able to double our lead just before the break, when a speedy counter-attack led to Bernardo Silva smashing an emphatic volley past Emi Martinez, giving us a comfortable cushion going into half-time.
Our lead was halved just a few minutes into the second 45 though when Ollie Watkins swept home from a corner, and our defence had to be at our best as the spirited hosts searched for an equaliser.
However, we stood strong to nullify any threat from Villa, holding out for a potentially crucial three points in the Premier League title race.
View the best images from our Midlands clash via the gallery below.