Craig Bellamy was controlling this contest at Fratton Park even before Pompey took a surprise eighth-minute lead through Nadir Belhadj.
West Ham desperately needed these three points but the cold turkey was digested before the 3,000 travelling fans even had a chance to celebrate.
Bellamy, 29, has been told by the club that he could be sacrificed in next month's transfer window with Tottenham looking his most likely destination if the Spurs board can put together a tempting enough deal.
The Hammers got their game together early on as the spine of Robert Green, Matthew Upson, Scott Parker and Bellamy comfortably guided their side to victory against a Pompey side that looked short of confidence.
The prospect of any of those players departing will certainly leave West Ham facing a massive battle to stay up.
They equalised in the 20th minute when teenager Jack Collison met Mark Noble's cross and his side-footed strike went in through David James' legs.
Jermain Defoe missed a penalty before half-time as the Hammers sensed they might benefit from some overdue good fortune.
After the break, further goals by Carlton Cole and a fine double strike by Bellamy wrapped up a convincing win for Zola's side.
For all West Ham's off the field problems, the same can be applied to Portsmouth. They too look like losing players in the window and their defence, so consistent last season, was hit time again on the counter-attack.
Boss Tony Adams is confident his side will recover their form soon enough. Their next destination: Arsenal away.
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