Carlos Pavon missed an 87th minute penalty for Honduras that would have levelled the game and left the United States needing a result in their final match against Costa Rica in Washington on Wednesday.
However, the victory guarantees the United States will return to South Africa, where they reached the final of the Confederations Cup in June, having earned a spot in their sixth successive finals.
Honduras began the game with the chance of booking a place in the finals themselves but they now have to win in El Salvador in their final game to have any chance of automatic qualification.
Having fallen to fourth in the group, which brings a play-off against the fifth-placed team in South America, the Hondurans must win and hope Costa Rica fail to win away to the United States if they are to take the third automatic spot.
The result was hugely disappointing for a country dealing with political tensions following a military coup and, in purely sporting terms, searching for their first World Cup appearance since 1982.
But a defeat did not look on the cards judging by the early exchanges, with Honduras piling on the pressure and then taking the lead a minute into the second half through a superb free-kick from Julio Cesar de Leon.
Roared on by a passionate home support, Honduras went looking for a second but were hit by three goals in 17 minutes from the United States.
INSPIRATIONAL CHOICE
First Casey, a surprising but inspirational choice by coach Bob Bradley to partner Charlie Davies in attack, headed an equaliser when he outjumped keeper Noel Valladares after Davies had flicked on a long ball.
Then Landon Donovan split the Honduran defence and Casey showed a cool touch to convert.
Donovan then turned finisher with a curling free-kick from 20 metres out to make it 3-1 although Valladares appeared at fault for his positioning.
At 3-1, Honduras looked a spent force but they regrouped and found a way back through a close-range effort from De Leon in the 79th minute.
Jonathan Spector was then ruled to have handled in the area but Pavon blasted the penalty high over Tim Howard's crossbar and minutes later the big striker missed a close range header to cap a night he will want to forget.
The defeat was the first home loss suffered by Honduras in the qualifying campaign, a fact not lost on a beaming Donovan.
"It's about having guys who can go out there and do the job. This is not an easy place to come and win at - no one has won here in qualifying and we just have, that tells you something," he said.
