The League One side pulled off a major shock in ousting Chelsea in the previous round, and they accounted for top-flight opposition once more at Valley Parade on Sunday.
John O'Shea's early own goal gave them the ideal start, before former Sunderland man Stead continued his record of having scored in every round of this season's competition with a low shot just after the hour.
"It was a terrific start to get the goal and we carried on from there and did the right things," Stead told BBC Radio 5 Live.
"I couldn't move in the last five minutes but everyone put a shift in and we've done it again and we're obviously buzzing.
"I'm just looking at that wall of supporters and it's absolutely incredible."
"It was thoroughly deserved, the boys performed fantastically well," added goalkeeper Williams.
"It's fantastic for everyone involved. The boys don't need any encouragement, we're playing against brilliant opposition and we're all up for it.
"Everyone ran their socks off and worked hard and it's thoroughly deserved. We'll take anybody at home [in the next round]. The quarter-finals is a massive bonus for everyone."
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