A first-half goal from Adam Johnson secured the three points for the Black Cats and provides them with real hope of remaining in the Premier League next season.
Early in the second half, Steven N'Zonzi was shown a second yellow card and sent off for Stoke, meaning the remaining minutes didn't pass without a few scares for the home support.
Speaking to Sky Sports after the game, Oatway said he thought his side deserved the victory.
The 40 -year-old said: "The gaffer wants us to play decent football.
"But at times it isn't going to work like that and at certain times today it was about us being men and grinding out results and the boys were so that's all that mattered today."
Gus Poyet watched the game from the sidelines, but didn't attend the post-match interview due to illness.
And, because of the result Oatway said the three points would be the perfect remedy.
He added: "I think he'll be a lot better after that.
"He's not been the best to be fair to him but I am sure this result will do him good."