United take on former Blades defender Chris Wilder's in-form Oxford - unbeaten in their last 10 matches - at the Kassam Stadium on Saturday and Wilson admitted his side will have to be at their best to avoid possible embarrassment.
"This is when the upsets happen isn't it?" said Wilson. "This is when the big boys will suffer and we've got to make sure it's not us.
"From Oxford's point of view they've got a great tradition in the FA Cup, a great history of knocking bigger clubs out so we have to make sure we don't join them."
Wilder, who made over 90 first-team appearances for the Blades during a six-year stint at the club, will be determined to ensure his side put on a better display than they did in the first round of the competition last year at Bramall Lane when Wilson's side ran out comfortable 3-0 winners.
"You'd be foolish to think it would be the same this time round," Wilson added. "A lot of personnel have changed anyway, but I don't think Chris' commitment has changed.
"They'll finish in the top seven in my opinion. I've heard good reports about them as well, particularly recently. There will be loads of people putting money on Oxford, they'll see it as a potential banana skin and we have to make sure we haven't got egg on our faces on Sunday morning."