The defender’s opener and Bernardo Silva’s stunner earned the champions a 2-1 win at Villa Park on Wednesday.
It meant they kept pace with Chelsea, who won 2-1 at Watford, and sit second, a point behind the leaders.
They did it without Kevin De Bruyne, John Stones, Ferran Torres and the banned Aymeric Laporte while Phil Foden was an unused substitute having missed the last two games.
It was also boss Pep Guardiola’s 150th Premier League win as he became the quickest manager in the competition’s history to hit the milestone, in just 204 games.
“That’s who we are, that’s what our team is made of,” Dias told the club’s official website.
“Big shout out to everyone because to come here and perform how we did is a demonstration of how we work, no exceptions.
“The bigger the challenge the bigger the wins. We love that. It is what we are here for.
“Bernardo’s goal was even more special because it gave us the 2-0 lead. It gave us a little bit of extra confidence into the second half.
“The game changed when they scored. We have to give them credit because it was a good goal. It changed the game, they went with the crowd, but our team were always there and we were always in control.
“It is a very important win against a team that are on fire under a new manager. It was very important to get the three points. Everyone fought a lot and we are very happy.”
After Ollie Watkins’ goal two minutes into the second half mid-table Villa improved having been given the run-around before the break and made City work for their victory.
The bigger the challenge the bigger the wins. We love that. It is what we are here for
Only Ederson’s save from Carney Chukwuemeka with 15 minutes left ensured City left with all the points.
“Against a really good side, I thought in the second half we were really good,” defender Matty Cash told VillaTV.
“I think in the first half we were a bit passive in some areas but the reaction we showed after half-time was really good.
“We were unlucky not to get a result, really. They’re a top-quality side so we’ve got to take that performance in the second half into the weekend.”