Under Nigel Clough, the Blades have lost just once in 17 outings in English football’s two main Cup competitions.
It is a record that would be impressive for the manager of Chelsea or Manchester City, never mind a club that has been in League One since 2011.
As part of that run, United have claimed five Premier League scalps inside a little over a year and Baxter, who has featured in all but one of those 17 Cup ties under Clough, believes a key factor has been top-flight clubs having to step outside their comfort zone.
He said: “You look at the Premier League and it’s all nice football. Marc McNulty, our striker against Southampton, is a prime example.
“Just clipping the ball down the channels and getting into the centre-halves, I think they were a bit shocked by that.
“They don’t really get that in the Premier League, everything is to feet and nice. They don’t really touch each other and it is not like that in our league.
“The Premier League is an unbelievable league, probably the best in the world. But those teams aren’t used to getting barged about, (having) people in the faces, kicking them and not helping them up when they get kicked. It works for us.”
Southampton and West Ham United, third and seventh in the Premier League, have both succumbed to United this season along with QPR, while Aston Villa and Fulham were both beaten last term.
Baxter added: “There is a bit of an aura about us in the Cups. Once you beat the big teams, your confidence grows. The more big teams that come to Bramall Lane or we go to them, they will be wary because we have knocked a few big teams out.
“If you think you just have to turn up to beat a League One team, then you’ve got another think coming.
“We have obviously got respect for Spurs, but we will go out there to boss them about and do things to them that Premier League teams don’t do.
“Our run increases our belief that we can beat anyone in the cups and we showed that last season too. Look at Southampton, they have beaten everyone in the league and are high-flying in the Premier League. So, for them to come here and for us to beat them shows we can really beat anyone.”