Despite being forced onto the back foot, the Blades pulled themselves level on the stroke of half time through Ben Brereton Diaz, who celebrated his Premier League debut with a goal.
After going into the break on level terms, Sheffield United carried the greater threat in the second period until they were dealt a sucker punch in the 78th minute when James Ward-Prowse restored West Ham's advantage from the penalty spot.
However, the drama was far from over as Rhian Brewster and Vladimir Coufal were both given their marching orders, before Oli McBurnie netted a 103rd-minute spot-kick to ensure the contest ended all square.
Although they salvaged a point, the Blades remain rooted to the bottom of the Premier League table, while West Ham stay in sixth position.
More to follow.