Half-time sub Oli McBurnie was the Blades' hero as he kept his cool to convert a penalty in the 13th minute of stoppage time, after being clattered by Hammers goalkeeper Alphonse Areola four minutes or so earlier.
Earlier Ben Brereton Diaz had cancelled out Maxwel Cornet's opener with a goal on his Premier League debut but James Ward-Prowse looked to have won it for West Ham with a 79th-minute penalty, after Gus Hamer brought him down. Blades sub Rhian Brewster saw red for a out-of-control challenge on Emerson Palmieri but United stuck to their task and got their reward deep into stoppage time.
Here's how we rated the Blades' players on a topsy-turvy afternoon...
Here's how we rated the Blades' players on a topsy-turvy afternoon...