But when Kamara kept his cool to give Fulham the points, Hodgson and his staff leapt from their seats in joy.
City started sleepily in the spring sunshine at Eastlands as Fulham created early chances; Clint Dempsey forced Hart into a diving save from Simon Davies's pull-back after Jimmy Bullard's long-range effort dipped wide.
But Ireland's goal was the catalyst for a change in the balance of play as Fulham's optimism crumbled in the face of a slick City onslaught.
When Benjani slid his shot home on 21 minutes, the writing appeared to be on the wall for the visitors.
Interview: Man City boss Sven Goran Eriksson
Elano was somehow running the game from right-back, picking out Vassell behind the defence and finding Petrov with some wonderful crossfield passes.
And when Fulham finally did create a chance - Northern Ireland striker David Healy meeting Simon Davies' cross with a point-blank header - Hart made a fine one-handed reflex save.
Fulham have been stuck in 19th place in the table since the New Year, and with Birmingham two ahead against Liverpool, their long-suffering fans fell silent.
But when Murphy put them level after Hart had blocked his tame spot-kick as Liverpool drew level at St Andrews and Bolton failed to hold their lead at Tottenham, they finally found their voice.
A draw, however, was not enough for Fulham and as they pressed forward a fine ball picked out Kamara in the inside left channel and he lashed powerfully into the roof of the net to leave Eriksson shaking his head in disbelief.
Manchester City manager Sven-Goran Eriksson: "We lost a game we should have won. We controlled most of it, and we thought it was done.
"If you don't defend, you lose the ball and you give them chances. They fought until the end, but we stopped fighting.
"We can't blame anyone but ourselves for losing a game like this."
Fulham manager Roy Hodgson: "It was a splendid victory for us, one we so badly needed.
"It looked bleak at half-time, and we had a mountain to climb - we didn't deserve to be losing. But we did it.
"At 0-2 I honestly thought we weren't out of it. I never lost hope, but to win it was extraordinary. We've given ourselves a chance now."
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