On-loan from Torino, the Italian hit-man shot down the Magpies with a double-barrelled blast and generously made a third goal for Matthew Etherington, before Michael Owen netted a late consolation on another nightmare afternoon for Newcastle United.
Last week, 48 hours before he was officially due to move into the manager's office at Upton Park, Zola had sat in the stands at West Bromwich Albion, watching a suicidal West Ham United side hand the bottom-placed Baggies their first victory of the season.
Seven days on, he was clearly determined that there was to be no repeat and, installing himself in the Hammers hot-seat for the first time, the Italian made three changes as Di Michele, Julien Faubert and Etherington came in for Dean Ashton (ankle) and substitutes Calum Davenport and Luis Boa Morte.
In the opposite dug-out, Chris Hughton had already endured a baptism to forget as the Magpies' makeshift manager and, following last weekend's harrowing home defeat at the hands of Hull City, the ex-West Ham defender made two switches.
Damien Duff and Fabricio Coloccini came in for Shola Ameobi and Danny Guthrie, who was suspended as a result of his lamentable, leg-breaking tackle on the Tigers' Craig Fagan.
The Hammers may have been pointless on their travels but on the green, green grass of Upton Park, they kicked-off looking for a third successive home win of the new campaign and, indeed, they were soon ahead, once more.
With just eight minutes on the clock, Carlton Cole invited Di Michele to cut in from the right, skip past Coloccini and then unleash an 18-yarder that deflected off David Edgar, before looping over the stranded Shay Given.
Mark Noble then sent a couple of 20-yard free-kicks over the angle, while the industrious Cole fired just wide from similar range as West Ham, playing free-flowing football with pace and purpose, eagerly went in search of their second.
As the half-hour approached, Owen diverted a header beyond the far post but that was mere token resistance in an opening period dominated by a Hammers side that was simply enthralling the home fans amongst the shirt-sleeved crowd of 34,743.
Indeed, ten minutes before the break, Di Michele took another step towards entering East End folklore, when Noble sent him clear and, although Given parried his first shot, the inventive Italian was first to the loose ball, and after lifting it over Steven Taylor on the edge of the six-yard box, he fired home as Coloccini arrived on the scene a split-second, too late.
Just after the break, Geremi's hopeful cross from the right flank sailed just beyond the far post and then Owen wastefully headed straight into the hitherto redundant Robert Green's hands from close range.
But on 53 minutes, all hopes of a Tyneside turnaround evaporated, when that man Di Michele burst down the right wing and unselfishly squared into the six-yard box, where Etherington stole in front of Edgar to give the Hammers a three-goal advantage.
On the hour mark, Di Michele should have claimed the match-ball but with time on his hands he impatiently blasted over from 15 yards as the muddling Magpies defence just stood and stared.
Midway through the half, however, Owen reduced the deficit when he collected Claudio Cacapa's precision pass and beat Green with an equally inch-perfect, low, curling 18-yarder.
The Hammers keeper then had to be at his best to foil both Cacapa and Duff but, on an afternoon that belonged to Zola and the on-fire Di Michele, time simply ran out for the beleaguered Geordies and their long-suffering supporters, who could have suffered an even worse fate had Boa Morte not incredibly missed an open goal in stoppage time.