Another day, another remarkable result in the capital. If Boris Johnson can be elected mayor of one of the world’s great cities, Fulham can surely escape relegation. They will take that fight to the last game after a thoroughly deserved defeat of Birmingham, who, on this performance, would have to be favourites to go down.

Birmingham must beat Blackburn at home next Sunday, and hope; Fulham will travel to Portsmouth, their fate in their own hands, and confidence coursing through every vein.

“Relief, satisfaction with the team’s performance and admiration for their mental courage,” said Roy Hodgson, when asked what his feelings were at the final whistle. Pride must have been there, too. Not only did every player win his individual battle, they all played with purpose and passion to register their first back-to-back victories in 70 Premier League outings, rising above the frantic atmosphere by outpassing as well as out-hustling their opponents.

The primary responsibility for that fell on Danny Murphy and Jimmy Bullard. The two midfielders dictated play from the start, creating space with neat triangles. With Simon Davies and Clint Dempsey offering width and Paul Stalteri and Paul Konchesky supporting the wingers from the back, they had options. City goalkeeper Maik Taylor had already had to help a Brian McBride header against the bar – it wouldn’t have counted; the American striker had been incorrectly flagged offside – when a clever free kick saw Bullard sucker the Birmingham defence by pulling the ball low across the penalty area for Davies.

Unmarked, about 10 yards out in the centre of goal, he hit his shot firmly, only for Taylor to dive to his left to make a fine one-handed save.

The danger came when attempts to pass their way through the visitors’ defences resulted in turnovers.

Twice in the first 20 minutes apparently straightforward passes went astray, and when Birmingham got a chance to break, they did so in numbers. It took last-ditch interventions by Brede Hangeland and Aaron Hughes to prevent Mikael Forssell having clear shooting opportunities.

The replacement of the reliable Liam Ridgewell with Franck Queudrue in the centre of the Blues’ defence at half-time was not a change Birmingham manager Alex McLeish had wanted to make.

The Frenchman has spent most of his career at left-back and City paid heavily for his unfamiliarity with the position.

Bullard’s free kick from the left was hit from far enough out to make the defender favourite to clear, but somehow Queudrue lost McBride, as well as the flight of the ball, and the forward dived to head beyond the helpless Taylor.

Fulham almost had a second when Diomansy Kamara embarked on one of those runs when it looks as though the ball is glued to his instep. Having left two defenders on the ground, this most frustrating of players did what he so often does, wasting his good work by blasting wildly over.

McLeish reacted by sending on the young Argentine forward Mauro Zarate for the ineffectual Olivier Kapo and going to three up front, but Hodgson, aware that Fulham had kept only five clean sheets in their previous 36 Premier League games, continued to encourage his players to look for a second. Their cause wasn’t helped when Kamara limped off, replaced by Erik Nevland, but they still looked the side more likely to score.

With 15 minutes remaining, Dempsey arrived late to head over as McBride, who surely would have scored, was left to look on, agonised.

McLeish then played his final card, Cameron Jerome replacing Forssell, but Queudrue was still a liability. His hapless attempt to head Konchesky’s long ball back to his goalkeeper was seized on by Nevland. The striker accelerated away from Radhi Jaidi and beat Taylor decisively. The Birmingham players’ heads dropped, their frustration evident in a number of bookings for dissent in the final minutes.

“It’s euphoric out there at the moment and I’m happy about that, but it could turn into sadness if we’re not capable of beating Portsmouth and end up relegated after all,” Hodgson said. “If that does happen, at least we’ll have shown we went down fighting and trying to play our way out of it.”

McLeish did his best to sound upbeat. “It goes to the wire and we have a lifeline next week,” said the Scot. “The players gave me everything. Now we have to beat Blackburn, which won’t be easy, but the players know what’s at stake.”

Three points may not yet be enough to save them, though, and although Blackburn are out of the running for the Uefa Cup berth, the odds are that Birmingham will be heading back to the Championship.

Match stats

Star man: Simon Davies (Fulham)

Player ratings: Fulham: Keller 6, Stalteri 6, Hughes 6, Hangeland 7, Konchesky 6, Davies 8, Bullard 7 (Andreasen 88min), Danny Murphy 6, Dempsey 6 (Healy 90min), Kamara 7 (Nevland 67min), McBride 7
Birmingham: Taylor 7, Kelly 6, Jaidi 5, Ridgewell 7 (Queudrue ht, 3), David Murphy 5, Larsson 5, Muamba 5, Johnson 5, Kapo 5 (Zarate 58min, 6), Forssell 5 (Jerome 74min), McFadden 6

Yellow cards: Fulham: Stalteri, Davies Birmingham: Muamba, Jaidi, McFadden, Queudrue, Jerome

Referee: C Foy

Attendance: 25,308

Fulham back from the dead

Fulham have a fighting chance of survival after three wins in their past four matches. They will need a win at Portsmouth next Sunday to be sure of staying in the Premier League, although a draw might be enough. Derby are relegated, but the two clubs who drop into the Championship with them will not be decided until the final day of the season. A point for Bolton would keep them up. Birmingham will stay up with a draw at Blackburn, providing Reading and Fulham lose their final games

Remaining fixtures in the relegation battle: May 11 (all 3pm) Chelsea v Bolton Wanderers, Portsmouth v Fulham, Derby County v Reading, Blackburn Rovers v Birmingham City