The victory and the priceless three points will give Charlton hope that they can avoid the drop, but on this display West Ham now look doomed to Championship football next season.
Charlton stormed forward from the opening whistle and took the lead on 24 minutes when the West Ham defence was split open and Marcus Bent crossed from the right for Darren Ambrose to fire home from close range for Charlton's first Premiership goal in 282 minutes of football.
There were gaping holes in the visitors' defence and they conceded a second goal while Charlton only had ten men, with Marcus Bent having limped off with a hamstring strain.
Winger Jerome Thomas took on two West Ham defenders before planting the ball past Robert Green for his first goal for a year.
The only response from the Hammers was a Nigel Quashie shot, which tipped over the bar by Scott Carson.
Charlton put the result virtually beyond doubt four minutes before the break when Darren Bent, back in the side after an eight-match absence through injury, was put through by substitute Jimmy Floyd Hasselbaink to fire home his 11th goal of the season.
Hasselbaink hit the post early in the second half, before West Ham attempted belatedly to get back into the game and Carlos Tevez saw his free-kick tipped over the bar by Carson, who then saved well from substitute Marlon Harewood.
But still it was Charlton, brimming with confidence, who continued to dominate the game and they put the icing on the cake for their best win of the season with a fourth goal and a second for Thomas as he scored from close range from a cross from Ambrose and with almost the final action of the match Chinese international Zhi Zheng headed a free-kick against the West Ham crossbar.
The two sides had gone into the match with identical records, five wins, five draws and 17 defeats, and was six points adrift of fourth-bottom Wigan who play at home to Newcastle on Sunday.
Since Curbishley's arrival at West Ham his side have won only once in ten Premiership games and have scored only 18 goals all season. They were the only Premiership side without an away win and on the evidence of this performance, will struggle to pick up any points on their travels.
They were awful in the first half and appeared to lack the stomach for a fight, in contrast to Charlton who went to Spain for a week to reach peak fitness and the trip certainly paid dividends for them.
With a match against fellow strugglers Watford away next week they will feel supremely confident of getting out of trouble if they can produce this kind of performance again.