They may well stay up this season, by default perhaps, with the three sides below them appearing incapable of hauling themselves free, but it will feel hollow.
This wasn't just a defeat, it was a humiliation, a ragged capitulation. Frustrated home supporters sang bitterly of players not fit to wear the shirt, of a manager being sacked in the morning.
It's unlikely that chairman David Sullivan will be able to persuade Straumur, the bank that still owns half of West Ham, to sanction that if it is what he wants to do, but Zola is a man who will have felt crushed by last night's events. He may walk. Possibly.
In the wreckage around West Ham it shouldn't be forgotten that Wolverhampton Wanderers played with a hunger, a desire, a will and skill that hollered of a team that is desperate to stay in this division and are set to do just that.
West Ham weren't. They were desperate, sure, but in a way that spoke of belief being drained.
A hug between the two managers a couple of minutes into the encounter, the initially sparring under way, betrayed the nerves.
Those nerves quickly showed again. It was only a routine punt forward by Marcus Hahnemann but it was headed on by Kevin Doyle and suddenly Kevin Foley had stolen ahead of Fabio Daprela.
With the young full-back desperately trying to retrieve matters, Foley struck a fierce, angled right-footed shot that rattled the crossbar with Robert Green clutching air.
There was a clear division of confidence. After four successive defeats, West Ham were drained. Four points from their last two away matches, including that spirited draw against the other claret and blue side, Aston Villa, meant Wolves were pumped.
Still Zola was able to bring back four players, chairman David Gold had referred to how he had 'carefully managed' his squad i.e. rested against stronger opponents and half-chances were created for Julien Faubert and Carlton Cole.
But it was Wolves who carried the greater threat, the greater bite. And, suddenly, they also had the lead. It came through Doyle's prodigious work-rate and a horrendous error, by James Tomkins. All it took was a long ball forward, Doyle chased it down but Tomkins, clearly, had the advantage.
He hurried his back-pass, mis-hitting it disastrously, falling short and Doyle ran through to calmly shoot across Green and into net.
West Ham, stunned, needed a response and when Benni McCarthy twisted and turned he passed up the chance to shoot himself only to tee up Carlton Cole whose sidefooted effort lacked power and was easily fielded by Hahnemann.
The crowd had been quietened; expectation dampened; trepidation rose. Doyle was the wrecking ball. He was occupying the West Ham defence, spreading uncertainty by his tireless presence, perpetual motion, deceptive pace.
But it was when David Jones, on the corner of the area, was kicked by Radoslav Kovac that Wolves, probably rightly, howled for a penalty only to be waved away by referee Phil Dowd.
West Ham were being run ragged. Wolves zipped the passes and Green was scrambling again to try and cover Jones's deflected shot. On the day that
West Ham formally submitted their plans to take up occupancy of the 2012 stadium, here they were struggling in the foothills rather than trying to reach those Olympic heights. It appeared a pipe dream.
On half-time there was a flicker of hope and it came from West Ham's great hope, the returning Scott Parker who, in trademark fashion collected the ball and barrelled into the area to arc a low shot around Hahnemann.
It struck the post. Parker quickly collected the rebound and from the tightest of angles shot goalwards only for Hahnemann to, brilliantly, block on the line. The ball was hacked away.
Tellingly Tomkins was withdrawn, one of two changes but they struggled to change the momentum. Alessandro Diamanti flickered but it wasn't happening.
Not for him, not for McCarthy, not for Cole. And so Wolves scored again. Again it owed much to their determination with Jones reacting quickly to hold off Matthew Upson and slice the West Ham defence with a low pass to Ronald Zubar.
Sprinting clear on the right he struck a shot, deflected, across Green who was beaten by the power. It was his first Premier League goal. Good timing.
West Ham collapsed. A long ball from George Elokobi, taken by Jones and, once more, the midfielder dissected the defenders with Matt Jarvis running on to beat Green once more. Cue an exodus of home support.
Zola threw on his final substitute, Guillermo Franco and, with a rasping drive, he drew a fine save from Hahnemann and then, in injury-time, he lifted Valon Behrami's pass into the net. It was no consolation.