Dias powerfully headed in his first goal for City on the half-hour mark and Stones struck the winner with just over 20 minutes remaining after Michail Antonio equalised for the visitors just before the interval.
The duo has become well-known for their defensive solidity in recent months, but it was their attacking exploits that earned City all three points at the Etihad Stadium.
Stones, who scored his fourth goal of the season in all competitions, had nothing but praise for the Portugal international after the victory.
"You can only give credit to him for moving countries, coming to a new club and playing the way he’s played straight away," he said. "He’s been outstanding and that’s just down to him. It’s a massive credit to him.
"We try and chip in and everyone’s out there working hard. Sometimes it doesn’t come off for the striker but today me and Ruben chipped in. That’s part of us being such a good team, and such a collective in big games.
"Everyone chips in or sometimes the person you don’t expect steps up and today it was me and Ruben. I’m glad to get the three points and keep the run going."
The visitors made it a tough afternoon's work for City and showed plenty of attacking threat, striking the outside of the post and also forcing Ederson into making saves.
And Stones feels some credit has to go to David Moyes' side.
"Yeah, they did make us work for it," he said.
"A lot of credit to West Ham. We knew what they were coming here to do. Their position in the table speaks for itself.
"They gave us a great game today. We had to fight right until the last few minutes. I’m really satisfied.
"At half-time, we were a bit deflated after conceding late in the first half. We weren’t at our free-flowing football that we’re used to in recent weeks but that’s again how they set up against us.
"We showed great character from half time and through the second half."
The victory takes City 13 points clear at the top of the table and Pep Guardiola's side are still competing in all four major competitions, but Stones feels that the team need to remain grounded and focused.
"We knew that we had to take it each game at a time, we knew our quality. We come about our business in our own way and we keep fighting.
"We set the bar so high in previous seasons and we want to get back there. We knew we had to fight, we have a bunch of fighters in the dressing room, everyone is playing games. It’s been an incredible few months and there’s still a few months left.
"We’re in every competition to try and win them. That is our target, with this mentality and spirit and hopefully, you never know what can happen."