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.
West Brom, led by midfielder Borja Valero, had bossed the game until that point and had wasted numerous chances to build a greater advantage.
But West Ham's leveller stunned them and they soon found themselves behind when they failed to defend a corner, Matthew Upson heading back across goal for Neill to finish smartly.
It provoked a half-smile from Zola, but his new side were about to show the defensive frailties that the former Chelsea striker would have exploited with relish in his playing days.
The unmarked Leon Barnett put pressure on Green, who fumbled and then tripped the Baggies man, leaving Bednar to demonstrate perfect penalty technique.
After such an incredibly open first half, it was always likely to be a tighter contest after the break - and so it proved.
Chances were now at a premium, as the midfield became congested and players scrapped for possession.
Keen was pleased with West Ham's performance
Bednar had a shot blocked and Barnett directed a header wide, while West Ham's attacking threat had virtually disappeared.
Yet there was to be one last twist when Brunt raced on to a long ball and fired accurately into the bottom right corner to snatch all three points.
Scott Parker should have equalised in injury time but was denied by Scott Carson at close range.
Zola will now be under no illusions as to the size of the task ahead of him, while West Brom have finally earned some breathing space and move off the bottom of the table.
West Brom boss Tony Mowbray: "It's good to get that first win, the longer you go without a win, the more psychologically it becomes difficult for the players.
"Today's game could have finished 5-5 or 6-6. But I am aware we have got to control the football match better than we did today.
"We've got the win and now it's important we get a couple more."
West Ham caretaker manager Kevin Keen revealed new boss Zola gave little away when he visited his players after the game.
"All he [Zola] said was, 'Unlucky, and I'll see you on Monday'.
"We should have got something out of the game. We gave away an early goal but we came back well, created some good chances to go ahead.
"The disappointing thing was we let them back in for their second goal and their equaliser too quickly."
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