Having made 11 changes at the break, West Ham had a good opening at the start of the second half through Stewart Downing, though the winger's effort from 25 yards sailed off target.
West Ham continued to force the issue, and they could have had a penalty on 72 minutes when Mohamed Diame was fouled in the box. However, the referee was quick to dismiss their appeals.
Despite plenty of pressure from the away side, Stevenage made it 2-0 with 12 minutes left to play thanks to a smart strike into the bottom corner from one of their trialists.
West Ham pulled one back through Matt Jarvis in the 84th minute, and they snatched a draw in the final moments as Downing nodded in from a Jarvis cross.