Sergei Rebrov hit a shot that Notts. County goalkeeper Saul Deeney could only parry into the path of the returning Bobby Zamora, who had a simple task to stroke home from close range.
Notts. County soon restored parity, however, when a long ball wasn't dealt with and Kelvin Wilson was able to head home after Richardson's header was pulled back by Glynn Hurst.
This reporter didn't see the build-up, trying instead to find out from club historian John Helliar if the 18th second goal that started the evening was West Ham's fastest ever.
The verdict? "Probably."
Worse nearly followed when Hurst, who once played against the Hammers for Emley, blocked an attempted clearance from Walker, found the ball at his feet with the goal gaping, only to panic and hit the side netting.
Ian Richardson, a West Ham fan who had always dreamed of playing at Upton Park, was booked for preventing Rufus Brevett taking a free kick.
The fans who booed him as he was carded probably didn't know he was one of them!
County had to reshuffle early in the second half when Mike Edwards was stretchered off to be replaced by Matt Williams and shortly after that West Ham took the lead again.
Sergei Rebrov started the move, Marlon Harewood set up Bobby Zamora who had cleverly dummied the ball, and he made no mistake in side footing home.
Once again, though, the lead was short-lived and, after Zamora was unluckily adjudged to have hand balled, the subsequent free kick set up Hammers fan Richardson, unmarked, to smash home into the top corner.
West Ham regained the lead, though, courtesy of Sergei Rebrov's first goal for the club.
He struck a 35 yard free kick round the wall and under the body of a diving - and, no doubt, disappointed - Saul Deeley.
Midway through the second half, Tomas Repka went off to warm applause to be replaced by Andy Melville.
Fate was proving unkind to Zamora as he looked for his hat trick; first, he wasn't able to convert an open goal when Harewood headed an Etherington cross into the six yard box and then, when Harewood had generously let him take a penalty which the latter had earned when pulled down by Ullathorne, he side footed the spot kick into the arms of Deeney who dived to his right.
There was a late scare when a Stefan Oakes free kick flashed just wide of Walker's right hand post.
Alan Pardew made six changes from the side that started against Ipswich on Saturday.
James Walker replaced Steve Bywater as he did in the last round, while in the outfield Bobby Zamora, Sergei Rebrov, Steve Lomas, Rufus Brevett, and Hayden Mullins came in to the starting line-up for Carl Fletcher, Teddy Sheringham, Calum Davenport, Chris Powell, and Luke Chadwick.
There was a minute's silence before the game in memory of Brian Clough and all of the players wore black arm bands as a mark of respect.
TEAM: Walker, Repka [Melville], Brevett, Harewood, Lomas, Etherington [Cohen], Rebrov, Mullins, Reo-Coker, Mackay, Zamora.
Subs unused: Bywater, McClenahan, Ashikodi.
Attendance: 11,111