Birmingham are facing a last-day battle for Barclays Premier League survival after Brede Hangeland's brace helped Fulham triumph at St. Andrew's.
The Carling Cup holders, lacking several key players through injury and suspension, produced their worst performance of the season to leave their top-flight status on a knife edge.
City are now level on points with Blackpool and Wigan, in 18th and 19th, and have to visit Tottenham next Sunday. Tangerines are away to Manchester United while Wigan travel to Stoke.
Fulham boss Mark Hughes would have expected a response from his side after the 5-2 home defeat by Liverpool on Monday.
But he could not have imagined his players having such a stroll to victory and only poor finishing prevented them from at least doubling the final victory margin.
The Blues defence was at sixes and sevens and could not cope with Bobby Zamora, Andy Johnson and Clint Dempsey.
They were not allowed to settle in midfield and posed the minimum of threat up front without the pace and energy of the injured Cameron Jerome as an outlet.
To add to their woes Lee Bowyer, Stuart Parnaby and Martin Jiranek all had to be substituted through injury and then Alexander Hleb limped off to leave them playing with 10 men for the final 13 minutes.
Dempsey missed a great chance to put Fulham ahead after two minutes.
Former City striker Andy Johnson sent a low ball across the six-yard area and Dempsey spooned his shot over the bar with the goal at his mercy.
Blues looked nervous and Ben Foster had to parry aside a massive clearance from Mark Schwarzer at full stretch.
