It was a tense affair and the crowed had to wait until six minutes before the break until the Blades took the lead. Michael Tonge lashing in a awesome free-kick.
Captain Phil Jagielka headed the home side a second lead on 68th minute when he headed home from a corner, and Jon Stead made it a Defender, Midfielder and Forward 1 2 3 when his single goal with twelve minutes remaining sealed all three points.
The win opens up a vital five-point gap between Sheffield United and West Ham and ended the visitors' hopes of a fourth successive win.
The team line-ups reflected recent form, with Sheffield United making four changes and West Ham content to name the side that won at Arsenal.
And the opening half was wracked with tension and short on quality, inevitably given the stakes.
Tevez curled a shot over the bar from 12 yards after creating an opening, before Sheffield United's Colin Kazim-Richards wasted a glorious opportunity.
He volleyed over wildly at the far post after Keith Gillespie's cross had evaded a succession of West Ham defenders.
The Blades broke the deadlock six minutes before half-time, Tonge powering an unstoppable free-kick high past Robert Green after Anton Ferdinand had fouled Christian Nade.
West Ham, inspired by Tevez, came out after the break with real intent as they went in search of an equaliser.
Mark Noble surged into the box, only to be denied by a brave tackle from Claude Davis, who was injured in the process and had to be replaced by Chris Morgan.
Lucas Neill was left holding his head in anguish after he was thwarted by a brilliant save from Paddy Kenny low to his right.
And on the hour, Tevez wasted West Ham's best opportunity, cutting in cleverly only to shoot over the top from 10 yards.
It was a costly miss, with Sheffield United crucially doubling their advantage after 68 minutes.
Jagielka met Gillespie's corner with a firm downward header that beat Green and flew in at an unguarded post.
And Stead wrapped up a vital victory with a brilliant solo effort 12 minutes from time.
It was all the striker's own work as the chased a ball into the right-hand channel before cutting in and drilling a 20-yard effort low past Green.