The normally reliable Hammers number one lost his grip in the wet conditions on the half-hour mark as he dropped the ball at the feet of Kevin Davies, who hooked it into an empty net.
• O'Brien: Hard work sealed win
Green then failed push a low shot wide enough, with Gary Cahill bundling in from close range.
The Hammers, who could have gone top of the table with a victory, got a lifeline through Carlton Cole on the hour, but substitute Matt Taylor made sure of an away win with a 30-yard free-kick four minutes from time.
The weather had cleared somewhat by kick-off - but the pitch remained sodden after the torrential downpours which had fallen over east London all morning.
The ball was moving fast on the slick surface, and West Ham were happy enough to work some quick passes.
The visitors, who started proceedings out of the relegation zone only on goal difference, sent in couple of high balls into the penalty area to test Green, in a sign of things to come.
The first decent opening came after 12 minutes.
Cole, the Hammers main attacking threat following injury to England striker Dean Ashton, collected the ball 25 yards out and made space for a shot, which flew just over the crossbar.
Bolton broke quickly and had a sight of goal themselves when Sweden forward Johan Elmander was slipped through, but his effort lacked any power to trouble Green.
West Ham threatened again when on-loan full-back Herita Ilunga burst into the left side of the penalty area and towards the goal-line before his low, angled effort was blocked by Jlloyd Samuel.
In the 29th minute, Valon Behrami tried his luck from 20 yards with a low strike which skidded off the wet surface and just wide of the left-hand post.
However, it was Bolton who took the lead on the half-hour following a bad error by Green.
The keeper came to the edge of his area to make what should have been a routine collection from a high ball.
However, the England squad man fumbled and promptly dropped the ball right at the feet of Davies, who hooked it into an empty net.
Before the Hammers had time to regroup, they were further behind.
A free-kick into the penalty area was headed out, but only as far as Gretar Rafn Steinsson, who sent in a fierce low strike.
Green got down quickly to make a decent reaction save - but the ball broke lose and Cahill was on hand to prod it over the line for his first Bolton goal since a £5million move from Aston Villa in January.
The home side were now well and truly shell-shocked, with Bolton pressing forwards at every opportunity.
Half-time could not come quick enough for Zola, who has his work cut out to avoid a first league defeat since taking over from Alan Curbishley last month.
West Ham looked to find an early way back into the match following the restart, but despite continued possession, the home side again lacked ideas in the final third.
However, only a stunning save from Jussi Jaaskelainen prevented them from pulling a goal back on 50 minutes.
Cole made space for himself to turn some 25 yards out and sent in a looping shot which flew over the Bolton keeper - but he somehow got his trailing hand to the ball and pushed it onto the post.
After Wales striker Craig Bellamy was sent on, the home side upped the pace, but too often gave away possession.
Gavin McCann almost wrapped things up for Bolton with a side-foot effort from 25 yards which skidded just wide.
Jaaskelainen spilled a long-range shot from Scott Parker, but there were no West Ham players following up - much to the despair of the Upton Park faithful behind the goal.
The Hammers then had a lifeline on 68 minutes.
Matthew Etherington's corner from the right was nodded back into the six-yard box where Cole arrived to head the ball in off the underside of the crossbar and chalk up a fourth goal of the season.
West Ham, buoyed by the home fans who had suddenly found their voice, pressed again as Behrami fired wide.
There was certainly more urgency about the Hammers now, if still lacking an end product.
However, Bolton sealed a first away victory of the campaign when substitute Taylor smashed in a 30-yard free-kick four minutes from time.
O'Brien: Hard work sealed winGianfranco Zola maintained goalkeeper Robert Green should not be made a
scapegoat for his first Barclays Premier League defeat as West Ham manager
against Bolton at Upton Park today.
The England man - hoping to be included in Fabio Capello's squad for the
forthcoming World Cup qualifiers to be named tonight - lost his grip in the wet
conditions on the half-hour mark as he dropped the ball at the feet of Kevin
Davies, who hooked it into an empty net.
Zola insisted: "I do not have to say anything to Robert Green. He is a great
goalkeeper.
"He has all my trust, all of the team's trust. Everyone believes in him.
"Today it has been a bad day, but I am sure next game he is going to save two
penalties - football is like that.
"The important thing is that you are always confident in what we are doing,
because they are the right things to do for us.''
The result, though, was a reality check for West Ham.
The were on the wave of euphoria which followed the appointment of the Italian
to succeed Alan Curbishley last month and back-to-back league wins - another of
which today would have, albeit briefly, put the east London club on top of the
table.
"When you find your team playing well, as we were before the goal, you expect
your team to score at any moment and instead when it comes from the opposition,
that is quite a surprise,'' said Zola, whose first taste of defeat had come in
the Carling Cup at Watford.
"But we have to improve and believe that it won't be like this every time.''
The Hammers boss added: "Everybody knew that it would not be so simple.
"The players need to improve certain things, you need to improve the
mentality.
"Sometimes games like this can help you make one step back in order to make
two steps forwards. I hope it will be like that.''
Bolton boss Gary Megson hailed his side's performance.
He said: "It was a great result for us, as was the manner in which it came for
us.
"However, we did not really have to deal with too many clear-cut chances.
"We wanted to make ourselves solid, and knew West Ham would have a lot of
possession - but most of that was going square or backwards. It did not really
cause us any problems - Jussi only had some long-range shots to deal with.
"Although they had more possession than us in the first half, it was us who
scored the two goals.''
Bolton had not won away since April 19, a fact not lost on Megson who believes
that form will be crucial to their survival chances.
He said: "The football club have not won away games on a consistent basis.
"That is something like only our fifth win in the last 22 months.
"If you are doing that, it is going to cause you massive problems, because
then you have to be successful at home.
"We just managed to stay up last year, yet our home record was only six points
different from when we had qualified for Europe.
"Our away record has been shocking and it is something we need to improve
on.''
Megson was pleased Taylor had silenced some of the crowd with his strike, the
former Portsmouth winger having come in for unnecessary jeers by a section of
the home crowd.
"I don't know why he was getting all that stick when he came on, but it was
nice for him to keep people quiet,'' said the Bolton boss.
"He has got a great strike and you do fancy him to score from distance.''
West Ham United 1 - 3 Bolton Wanderers
