Two first-half howlers saw the Hammers keeper hand goals to Kevin Davies and Gary Cahill and, although Carlton Cole pulled one back for West Ham midway through the second half, Matthew Taylor sealed victory for the visitors thanks to a blistering 86th-minute free-kick.
With a hat-trick of home wins from their first three outings at Upton Park, the fifth-placed Hammers were unchanged from the side that recorded their first away victory of the season at Fulham, last Saturday.
And their was little sign of the disastrous afternoon ahead of them as Gianfranco Zola's confident team kicked off in determined mood.
Indeed, Julien Faubert soon forced Jussi Jaaskelainen to save his early free-kick, before Mark Noble quickly went into referee Mike Dean's book for a skidding tackle on Gretar Steinsson.
Despite losing at Manchester United last weekend, Bolton - in 17th spot and pointless on their travels - were also unchanged and they should have taken the lead with a dozen minutes on the clock, but after being played in by Ricardo Gardner, Johan Elmander wastefully steered his shot straight at the relieved Green.
On 20 minutes, a quick-throw from the Hammers keeper allowed Noble to play in the supporting Scott Parker, who invited David Di Michele to bend a 25-yarder just inches wide of Jaaskelainen's right-hand post.
Certainly that free-flowing move typified the brand of total football that Zola has been trying to introduce down West Ham way and when Valon Behrami climaxed a similar raid with a rising 18-yarder, the East Enders among the crowd of 33,715 were sensing that a goal was not too far away.
Those rain-sodden supporters they were right. But sadly for them, it was Bolton who were destined to break the deadlock with two quick-fire goals that Green will not enjoy watching on the re-run.
On the half-hour, the Hammers' keeper dropped Jlloyd Samuel's hanging cross from the left under pressure both from his team-mate Herita Ilunga and Davies, and he could only look on in horror as the Bolton striker emerged from the unsightly scramble to hook the loose ball into an unguarded net and claim his fourth goal of the campaign.
And just three minutes later, when Davies nodded on Andy O'Brien's flighted free-kick, Green was left to bury his face in his white gloves once more, after he found Steinsson's blistering low shot too hot to handle and Cahill eluded Ilunga's lunge to bundle Bolton into a two-goal interval lead.
That double-whammy left West Ham with a mountainous second-half task, but within five minutes of the restart, only the woodwork prevented Cole from reducing the arrears, when Jaaskelainen athletically clawed the striker's looping 18-yarder onto his left-hand post.
Shortly afterwards, Craig Bellamy replaced Di Michele as Zola looked to keep up the attacking impetus and after the Bolton keeper saved Parker's stinging 20-yarder at the second attempt, West Ham did finally beat the flying Finn.
Midway through the second period, Matthew Etherington's corner was nodded on by Matthew Upson for Cole to claim his fourth goal of the season, with a header that crashed into the net off the underside of the crossbar.
Behrami then sent a 20-yarder whistling past the angle before Zola introduced teenager Freddie Sears in a desperate bid to find a late leveller.
But it was a Wanderers substitute who had the last word, when Taylor drilled a simply unstoppable 30-yard free-kick past the West Ham wall to seal Bolton's first away points of the season.