A 24th minute goal from Craig Reid, his 21st of the season, and a second-half penalty from Joel Byrom put Boro in control before Chris Beardsley wrapped things up at the death.
Victory ensured Stevenage, in sixth at the start of the day on goal difference ahead of Notts County with Carlisle a point behind, reached the play-offs and will face the Blades over two legs. And Smith has warned United they will get a baptism of fire when they arrive at Broadhall Way.
"The game will be quick, it'll be energetic, it'll be physical, it'll be up and at 'em and I'll have the guys on raw meat and razor blades all week. They'll be ready for them," he said.
"These moments don't come around all the time, you can't look into a crystal ball and see this occurring every year so while we're here we want to make and take full advantage of it.
"If we come close to playing the way we know we can we've got a chance there's no doubt about that. We've got no fear at all but we'll give Sheffield all the respect they deserve, but they'll know having been here before that this is a tough place to come and the evening games here offer something very special in terms of the atmosphere."