James McClean's goal early on settled the nervous tension around the ground, with the Irishman dispatching coolly on a sunny Staffordshire afternoon.
Mame Diouf then made the contest safe just before the hour mark, finding the back of the net with the help of a deflection from Jordy de Wijs, which sealed Stoke's first three-point haul of the Rowett era.
During a dismal day for Hull, Evandro found himself sent off by referee Darren Bond for reacting to a tackle from Joe Allen.
And Rowett feels the belief should be back with his players.
He said: "I think the fact that we've tried to stay calm... we've tried to give players an opportunity as well. I thought the players that came in today did well and gave us more physicality.
"I thought we should try to stay positive with the players and maintain a little bit of belief. We felt if we kept doing the right things and built on the first 25 minutes of Wednesday night's game and not focus on all the other things that happen, then we could get some form of reward.
"I think we did today, 11 v 11. I thought we were very comfortable, I thought Hull played their part but the sending-off allowed us to kill the game off.
"We can't be blase, we have to show confidence and belief from now on."
Hull's afternoon away from home went from bad to worse almost immediately after they conceded their second goal when Brazilian midfielder Evandro reacted to a strong challenge from Allen by landing his own tackle on the Wales international.
Hull manager Nigel Adkins was frustrated at the Tigers' display in the Potteries.
Adkins said: "We've come away from home and we've conceded a goal from a corner and we have to address that I feel.
"I felt David Marshall dealt with the first ball in, punched it really well. It's gone outside the penalty area and McClean has driven it back in, it's gone through two people's sets of legs, and the second one is deflected, so we didn't get the rub of the green.
"I think we started the second half well. I'm looking to make two substitutions - I have Will Keane and Nouha Dicko waiting to come on while I take off Evandro and Fraizer Campbell - but as they are stood waiting, Evandro gets sent off.
"Having wanted to get back into the game, we were 2-0 down with 10 men so it was always going to be challenging."