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...
5. Auston Trusty 6
Had a fantastic chance for the Blades in the first half when Hamer's corner picked him out with no defender near him but he could only plant his header into Areola's arms when he really should have tested him further. And the miss became even bigger about two minutes later when West Ham went ahead at the other end. Helped set up the equaliser with a lovely header into Osula's path | Getty Images
6. Vini Souza 6
The Brazilian did the 'ugly' side of the game well, putting his foot in and tracking runners and blocking shots before making the simple pass to someone who could use the ball more effectively. | Getty Images
7. Gus Hamer 5
Was a little sloppy in possession by his standards early on as he turned the ball over too often when attempting passes but a lovely-looking ball almost resulted in a chance for Brereton Diaz and he should have picked up an assist for Trusty's header. Took a booking for pulling back Fornals after a poor pass from Robinson put United in trouble and then was penalised for the decisive penalty after getting a touch on Ings' boot, rather than the ball, after the forward had burst through Robinson's tackle | Getty Images
8. Andre Brooks 7.5
Fresh from signing a new contract, the Sheffield boy lit up Bramall Lane with a lovely piece of skill to nutmeg experienced international Coufal and his impressive calmness on the ball, which he has shown since coming into the side earlier this season, was again evident here, even in the tightest of spots. Saw yellow in the second half for fouling Palmieri in his haste to get the ball and was later replaced as United sought an equaliser, but another excellent showing | Getty Images