Andy King scored the only goal of the game after just three minutes to give the Foxes a fourth victory from their last five npower Championship matches - a return which leaves them just four points behind sixth-placed Leeds.
But the Foxes were indebted to some excellent saves from goalkeeper Chris Weale as the Blades laid siege to the Leicester goal.
When asked if it was the most difficult game since he took charge of City in October, the former England boss said: "I think so. Difficult, very difficult. They are very aggressive, strong, very direct, and put a lot of tests on our backline and goalkeeper.
"So I'm extremely happy with three points here because we were lucky a couple of times, our goalkeeper made two excellent saves.
"It was a good win, I think a couple of months ago, we would have lost a game like this. I think we have started to fight better than we have done in the past, especially away from home, so it's very good for us. A little bit lucky but also some very good individual performances."
Source: PA
Source: PA