Zola watched his side throw away a lead and suffer defeat
West Brom won for the first time this season and left new West Ham manager Gianfranco Zola with lots to analyse after watching from the stands.
James Morrison headed the Baggies in front before Mark Noble tapped in a rebound from David Di Michele's header.
West Ham took the lead when Lucas Neill volleyed in from close-range before Roman Bednar levelled with a penalty.
A draw looked likely but Chris Brunt scored a late winner to hand Zola an unfriendly welcome to club management.
The victory prevented the Baggies from recording their worst start to a Premier League season, but for long spells it seemed they would not take advantage of a poor Hammers defence, which must have worried Italian Zola.
Mowbray was relieved to claim first win
The Italian, who officially takes charge of the team from Monday, will also be concerned about his attacking options after Dean Ashton was forced off through injury early on, although replacement Di Michele was instrumental in dragging his side back into the game when they looked in danger of being overrun.
Morrison had already put West Brom ahead after being allowed acres of space in the box while Robert Koren had missed an one-one with Robert Green when Noble equalised after Di Michele's header had been saved.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.