Following their second straight defeat, Stoke go to Middlesbrough next Saturday for the second time in just over a month, having won 5-0 there in the EFL Cup in August.
Hull return home to host bottom club Cardiff City, in another of the Saturday afternoon kick-offs.
Stoke City boss Narcis Pelach told BBC Sport:
"I was happy with the first half hour. We scored a nice goal from a set play.
"But we have to make the most of our chances and then we made mistakes.
"The first goal should not have been allowed. It was offside before the penalty was given. The second goal was our mistake.
"But I did not think it was that bad. Our heads went down after the third goal went in."
Hull City boss Tim Walter told BBC Sport:
"After conceding the goal, we stayed bright and showed a lot of courage and found better solutions.
"We have to make the most of the chances we created. It’s the hardest thing in football to do. Such a small goal on such a big pitch.
"I was actually happy with how we played last week. Now we’ve had more time together and that has helped a lot.
"It has helped the feeling in the group but we have always believed in ourselves. It’s all about mentality – and having the confidence."