The win was the Blades' first success in five away games and kept up their promotion push, although it spelt more problems for Carlisle manager Greg Abbott as his side continued their tumble down the table.
Wilson said: "It was a great scoreline and it puts us back in the swing of things. We know it's always dangerous against a team that's on a losing run, but we were strong and disciplined from the kick-off."
Carlisle staged a recovery in the second half when it looked for a time like they might salvage a point and Wilson said: "Our momentum went a bit, but give Carlisle credit.
"We caused them particular problems down their left-hand side, which is where two of the goals came from."
The Blades boss was concerned about the tackle on midfielder Kevin McDonald, which could put the player out of action for some weeks.
He said: "There has to be some redress because it was a heavy tackle and his ankle has swollen up like a balloon, yet a little tug or push gets the same punishment, which does not seem right.
"It looks like he could be out for a few weeks at least and we will have to assess the injury once the swelling goes down."