Two goals in the final three minutes of the first half turned out to be decisive, with Carlton Cole and then Matthew Etherington finding the net.
• Zola: Confidence boosting win
There was still time for Fulham striker Andrew Johnson to be sent off before the half-time whistle was blown and although the home side were back in the game on the hour mark thanks to Danny Murphy's penalty, there was to be no further scoring.
Zola was able to enjoy his second victory in the league since succeeding Alan Curbishley, although last week's 3-1 Upton Park success over Newcastle had been followed by a Carling Cup exit at Watford in midweek.
Fulham had been so dominant in the opening exchanges that there was no inkling of the series of mishaps that were to befall them.
Simon Davies was only inches wide with a fierce drive early on although former Hammer Bobby Zamora should have done better when he planted a header wide after Danny Murphy had picked him out in the box.
West Ham goalkeeper Robert Green had to come off his line to stop Johnson from latching on to a through ball and when the striker was booked in the 20th minute for a lunge on Herita Ilunga, Fulham simply carried on attacking.
Zamora poked wide, Johnson headed a Jimmy Bullard free-kick over and Brede Hangeland was also off target when Bullard's corner eluded the West Ham defence.
It seemed it would simply be a matter of time before Fulham took a deserved lead and Bullard, having first planted a free-kick over, was denied only by Green's agility when he beat the wall with another from almost exactly the same spot.
Green had been hurt by former team-mate John Pantsil's follow-up as he dived to his left to palm away and tempers boiled over briefly.
That was the case again in the 39th minute when another ex-Hammer, Paul Konchesky, hurt Etherington and was booked, although the left-back had certainly played the ball before catching his man.
Etherington recovered and promptly set up his side's 43rd-minute opener before scoring the second himself.
Cole was quicker to the ball than Hangeland to send the winger away down the right and when Mark Schwarzer spilled the resulting cross Cole was there for a simple finish.
Schwarzer had been a virtual spectator until then but within two minutes he was picking the ball out of the net again.
Mark Noble played a pass from his own half and Etherington used his pace to leave his challenger behind and beat Schwarzer.
And there was still time for Johnson to pick up his second booking for a lunge on Lucas Neill.
Schwarzer was the busier goalkeeper in the second period and was required to make saves from first Noble and Ilunga as the Hammers made use of their extra man.
Fulham had not given up however and were awarded a penalty in the 58th minute when referee Andre Marriner ruled that Zoltan Gera's header had hit Neill on the arm. Murphy made no mistake from the spot.
Zamora then got the slightest of touches from Bullard's free-kick after Scott Parker had been booked for felling Gera in the 68th minute.
But again the striker should have done better as he was just six yards out with the goal at his mercy.
Still Fulham came forward and Ilunga survived another penalty appeal after a Pantsil cross had hit him.
Zola replaced the ineffective David Di Michele with Craig Bellamy with a quarter of an hour remaining and the Welshman set up Cole for a curled effort that clipped the top of the bar.
Bellamy should have scored himself however when he spooned the ball over an unguarded net after Hangeland had blocked his initial effort on the line, with Schwarzer nowhere.
Zola: Confidence boosting win
West Ham manager Gianfranco Zola admitted he would have no problem being regarded as a lucky manager after his side won 2-1 at Fulham.
Zola said: "I don't know if we were lucky today, I will leave it up to others to judge. But when you win you need a little bit of luck. Certainly I am not one who regrets luck.
"I would like to have luck in every single game but we played a good match and had a few occasions in the second half to make it (the score-line) bigger. I would like to be lucky every Saturday.
"I have been working with this team for two weeks and they know what kind of football I want. They are doing very well and they will get much better.
"Winning away games like this will give them a lot of confidence.''
Hodgson was convinced referee Andre Marriner had got it wrong over Johnson's second yellow, awarded when he challenged Neill.
He said: "We think, having watched the video, that it was an unfortunate decision from the referee because it was Lucas Neill, having cleared the ball, who catches Andy Johnson. It was not Andy Johnson kicking him.
"Hopefully the referee will look at that and see that as well. He was trying to block the ball. Will we appeal? We'll see.''
Overall however, Hodgson had no complaints about his side's efforts.
He said: "It has to go down as one of those really weird games where you have to be satisfied with a lot of the things we did out there.
"I thought we played some excellent football but within three minutes, a game we looked like being able to win and certainly give a good account of ourselves, within three minutes everything changed.
"I as really amazed how the players in the second half showed their character and physical fitness to work as hard as they did and almost bring us back into the game.
"Unfortunately at this level of football, when you are two goals down it is not easy to come back, especially when you have 10 men rather than 11.''