Sam Allardyce accused some of his Blackburn Rovers players of being overweight this week, but El-Hadji Diouf and Jason Roberts proved that they have the stomach for a fight by scoring the goals that lifted their team out of the relegation zone at Craven Cottage last night.

“We are on the way up,” Allardyce said after watching his side climb to fifteenth place in the Barclays Premier League. “Coming back from a goal down is very difficult, but we showed commitment and quality. Winning is all that matters now and the way we won will give the players confidence for the rest of the season.”

Roy Hodgson, the Fulham manager, sprang a surprise before kick-off by resting Bobby Zamora. The former West Ham United forward, who has a hip strain, has scored only twice in the league since his £5 million transfer from Upton Park last summer and his place in the starting line-up was taken by Zoltan Gera, with Clint Dempsey stepping up to partner Andrew Johnson in attack.

Dempsey took only 98 seconds to make his mark by giving Fulham the lead before most Blackburn players had even touched the ball. The United States forward reached a speculative header from Danny Murphy before Christopher Samba and he used his first touch to take Ryan Nelsen out of the equation before scuffing a left-foot strike past Paul Robinson and off a post. “We made it very difficult for ourselves by giving away a goal like that,” Allardyce said.

The goal cleared Fulham’s heads after the 4-0 home defeat by Manchester United in the FA Cup on Saturday and they created two more chances in the opening ten minutes. Johnson just failed to make a telling connection with a clever back-flick by Dempsey in the eighth minute and then Simon Davies forced Robinson to make a smart save from his half-volley.

Stephen Warnock has been Blackburn’s best player this season and the former Liverpool defender came close to bringing the visiting side back on level terms with a left-foot strike from the edge of the penalty area that rolled away from the goal after hitting a post. With Warnock man-marking Murphy, the heartbeat of the Fulham side, Blackburn posed a threat only when long balls were played into the centre of the Fulham defence. “They played the long-ball game very well and forced us back,” Hodgson said. “We came up against a team who had more strength and energy than us.”

Diouf started the Blackburn fightback by stroking the ball past Mark Schwarzer in the 69th minute for a contentious goal — his first for the club — that was allowed to stand by Rob Styles. The Senegal forward was offside in the build-up to the goal but the referee decided that he was not interfering with play and was onside when Samba’s header landed at his feet in the six-yard box. “I’d like to see it again,” Hodgson said.

Having abandoned their 4-5-1 formation early in the second half, Blackburn poured forward in search of another goal and only a series of excellent saves by Schwarzer prevented Allardyce’s team from taking the lead, before Roberts had the final word.

The former Wigan Athletic forward beat Toni Kallio to a cross by Morten Gamst Pedersen before scoring with his right foot. “The result was thoroughly deserved,” Allardyce said. “I’ve been telling my players not to look at the league table, but they can look at the papers now if they want. We knew that we could put them under pressure if we scored. It’s a huge relief. Everyone has been talking about relegation, but we are a very good team.”

Fulham (4-4-2): M Schwarzer — J Paintsil, B Hangeland, A Hughes (sub: T Kallio, 77min), P Konchesky — Z Gera (sub: D Kamara, 79), D Murphy, D Etuhu, S Davies (sub: E Nevland, 90) — A Johnson, C Dempsey. Substitutes not used: P Zuberbühler, O Dacourt, J Gray, F Stoor. Booked: Murphy.

Blackburn Rovers (4-5-1): P Robinson — A Ooijer, C Samba, R Nelsen, G Givet — E-H Diouf, K Andrews (sub: B McCarthy, 56), Tugay Kerimoglu (sub: A Mokoena, 81), S Warnock, M G Pedersen (sub, D Dunn, 85)— J Roberts. Substitutes not used: M Bunn, Z Khizanishvili, C Villanueva, D Simpson. Booked: Diouf.

Referee: R Styles.