Tempers frayed both on and off the field as Chris Wilder exchanged words with his counterpart Lampard during what was a lively fixture between two of the Sky Bet Championship's top six.
The win, with goals from each of the three United strikers to feature, lifts them to fourth, while Lampard's Derby drop to sixth.
Billy Sharp opened the scoring after 41 minutes, before Harry Wilson levelled with a trademark direct free-kick.
The Blades kept pushing for the three points and they were rewarded with goals for David McGoldrick and Leon Clarke in what was a deserved victory for the home side.
And Derby manager Lampard said: "In the first half we played pretty well and had a lot of possession.
"We played well in the first half and then got ourselves back at 1-1 early in the second, but we didn't play well in the last part of the game and made mistakes which lost us the game.
"A great goal by Harry and we needed to own the game then and I fancied that we would do. But if you give simple goals away it changes the atmosphere and it made it very difficult.
"They're one of the best teams in the league and a difficult team to play against.
"It was two managers who were into the game and we needed a referee with a cool head and maybe some decisions were wrong in both directions.
"We've got a good squad of players and we're in a decent position but it could be better."