كتب : Omar AbdelAziz
Egyptian midfielder Ahmed Fathi did not appear for Sheffield as he was not selected by manager Neil Warnock in the 18-man squad for an unspecified reason.
Michael Tonge put the Blades ahead in the 33rd minute, Phil Jagielka doubled the lead on 68 minutes and Jonathan Stead added the third 12 minutes from time.
Sheffield's win lifted them off the relegation zone in the 17th place with 34 points, while the Hammers are still struggling second from bottom on 29 points.
Elsewhere, Arsenal came back from a 10th minute strike from Nicolas Anelka to beat Bolton Wanderers 2-1, thanks to goals from midfield duo Thomas Rosicky and Cesc Fabregas.
The victory erased the Gunners' fears of missing the last UEFA Champions League spot as they lie fourth with 59 points and one game in hand, five ahead of fifth-placed Bolton.
Aston Villa jumped from 14th to 10th place after stunning Middlesbrough 3-1 at the Riverside Stadium.
Goals from Craig Gardner, Luke Moore and Stillian Petrov cancelled out Fabio Rochemback's early goal.
Portsmouth beat Newcastle 2-1 at Fartton Park, while Reading edged past Fulham 2-1 at the Madejski Stadium courtesy of a 15th minute strike from Stephen Hunt.
Manchester City and Liverpool played out a dull 0-0 stalemate at the City of Manchester Stadium.