So victory at Craven Cottage was a blessed relief for the beleaguered Hammers.
Fulham started brightly before their indiscipline set in. Simon Davies went close with a 12-yard half-volley, as did Bobby Zamora with a close range header.
But despite Fulham's early dominance, the Hammers always looked dangerous on the break with Etherington in particular causing the home defence problems.
Johnson received his first booking midway through the first half for an awful late challenge on defender Herita Llunga.
Hodgson was downbeat after the defeat
Replays showed he was lucky to stay on the field and his challenge was not an isolated incident in a fiery opening 45 minutes.
Soon after, Fulham's John Pantsil followed through on keeper Robert Green who had bravely palmed Jimmy Bullard's low free-kick away.
The challenge upset the West Ham players, with Lucas Neill in particular taking issue with Pantsil.
Fulham defender Paul Konchesky was next in the book for a late tackle on Etherington, whose pace continued to cause Fulham problems, and it was his run that brought about the opening goal.
The pacy winger broke free down the right-hand side and sent in a low cross that keeper Mark Schwarzer spilled into the path of Cole, who tapped home for 1-0.
West Ham increased that lead a couple of minutes later with Etherington getting his reward for a fine first-half performance.
He latched onto Mark Noble's through-ball and out-paced the Fulham defence before beating Schwarzer to the pass and poking home into the unguarded net.
There was more trouble for Fulham before the break and it was no surprise to see Johnson receive his second booking of the half - and subsequent red card - for yet another late tackle, this time on Neill.
West Ham began the second half with attacking intent and Schwarzer was called into action twice, first from Noble and then from Llunga.
Matthew Etherington scored West Ham's winner
But it was Fulham who scored next and it came from the penalty spot.
Neill was adjudged to have handled in the area, although the decision looked harsh, and Murphy sent Green the wrong way to get his side back in the game.
It was the incentive Fulham needed and Zamora came close to equalising with a close-range header that he really should have done better with.
West Ham soon sent for Craig Bellamy and the substitute striker had a glorious opportunity to make the game safe, but his shot was blocked on the line by defender Brede Hangeland, with the Welshman firing the rebound over the bar.
The miss mattered little though as West Ham held on to secure a welcome three points.
Fulham boss Roy Hodgson: "I am amazed that we have lost because we created lots of opportunities.
"If you look at the possession statistics and that of the chances created it would be on our favour.
"If I could dismiss those three or four minutes when we conceded two goals and had a man sent off.
"Our work-rate after the break when we were down to 10 men was exceptional and we still created chances."
West Ham boss Gianfranco Zola:
"I think it wasn't luck, I think we played a good match. There was only one team that deserved to win and I'm pleased that it was West Ham.
"We kept our composure and in the end of the day, we came away with three points and nobody can say we didn't deserve it.
"After the week we've had, a victory like this away from home will give the players a lot of confidence
"I've been working with these players for two weeks now and I can't ask any more than what they are already doing."
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