The first half ended scoreless, with the Reds applying plenty of pressure and going closest to breaking the deadlock when Joshua Zirkzee kneed Amad's cross towards goal from close range, only to have it cleared off the line by former United defender Aaron Wan-Bissaka.
United continued to push after the interval and it paid off, with Diogo Dalot turning home a loose ball that found him on the end of a Casemiro shot.
The lead held until the 83rd minute, but the Hammers found a way through, with Soungoutou Magassa firing home a rebounded corner from close range, forcing the Reds to settle for a point.