Non-league Kidderminster Harriers were seconds away from one of the biggest shocks in FA Cup history until Declan Rice rescued West Ham as the Premier League side progressed to the fifth round 2-1 after extra time.
Chelsea also needed extra time and late drama to see off lower league opposition 2-1 to reach the last 16 after Plymouth missed a late penalty at Stamford Bridge.
Sixth-tier Kidderminster sit 113 places below David Moyes’ men, who are pushing for a place in next season’s Champions League.
But the fragility in the Hammers’ squad without Rice and Michail Antonio was exposed as Harriers were good value for the lead given to them by Alex Penny’s early goal for much of the 90 minutes.
The defender smashed into an unguarded after the Hammers failed to deal with Omari Sterling’s free-kick.
Moyes sent on Rice at half-time among five changes during the second half, but the home side looked set to hold on until the England midfielder took matters into his own hands.