Two goals in the final 10 minutes from the winger and Matt Jarvis prevented the League Two side from claiming a morale-boosting pre-season victory over the Premier League outfit
The Premier League side looked set to slip to an embarrassing defeat on Saturday at the Lamex Stadium after an unnamed trialist added to Tom Pett's opener to leave Stevenage scenting a famous triumph.
But West Ham showed good spirit to score twice in the final 10 minutes, Matt Jarvis and Stewart Downing sparing their blushes a little.
With the season set to begin in almost exactly a month, Sam Allardyce's men were aiming to fly out of the blocks after fielding a strong starting XI.
However, the exact opposite happened as Stevenage, relegated to League Two last season, began the game impressively.
The hosts created several chances during the opening exchanges and it was no surprise when they took the lead in the 31st minute, Pett sliding past Adrian.
Not content, Stevenage continued to press forward and almost doubled their advantage just before the break when Andy Bond rattled the woodwork.
Things went from bad to worse for West Ham after half-time, with a trialist finding the net following a neat turn.
Yet that goal seemed to finally spark some life into the visitors and Jarvis converted an 84th-minute diving header after Stevenage failed to clear Guy Demel's centre.
Downing then nodded home Jarvis' cross at the back post in the first minute of stoppage time to secure a draw.