An excellent save by Bailey Hall, who got down rapidly to turn Daniel Cummings’ low effort wide, was needed to make sure the visitors emerged unscathed from a strong opening by West Ham.
But, from there, Liverpool began to take control and Will Wright’s eyes lit up when Isaac Mabaya delivered a cross from the right, only for a defender to intervene with a crucial headed clearance.
Bradshaw so nearly opened the scoring in style shortly before the half-hour mark.
Quick feet enabled the forward to work space for himself around 20 yards out and he beat goalkeeper Finley Hooper with a superb strike, only for the effort to rattle the bar.
Bradshaw went close again shortly before half-time, with the No.11 getting on the end of a fine Mabaya delivery at the back post but being denied by Hooper.
Danns seemed certain to net when the loose ball fell into his path, though West Ham defender Callum Leacock produced a last-ditch block to ensure the scoreline remained level at the break.
Bradshaw continued his quest to score with another attempt from distance that went narrowly wide in the early stages of the second half.
Wright headed a Bradshaw cross over the bar as the pressure on West Ham’s goal intensified and Hooper was again called into action to palm away Michael Laffey’s free-kick.
Wright’s best chance of the evening followed quickly, the No.9 unable to get the required connection to divert Alvin Ayman’s delivery beyond Hooper.
West Ham successfully weathered that storm, however, and became the stronger, more dangerous side as the game neared its conclusion.
And, with five minutes remaining, the home team broke the deadlock decisively when Kerr’s attempt at a delivery to the back post found its way into the net.