The last time a Premier League side survived from a position as perilous as Fulham was when Roy Hodgson masterminded a miraculous escape in 2008. The odds on Felix Magath repeating the feat shortened somewhat after substitute Hugo Rodallega headed a late winner at Villa Park to lift the Cottagers off the bottom and set up a crunch meeting with 17th-placed Norwich City at Craven Cottage next weekend.

Rodallega, who hadn’t scored a Premier League goal in thirteen months, glanced a Lewis Holtby cross into the far corner four minutes from time and wheeled away to celebrate in front of 3,00 delirious travelling fans, who dare to dream of a second stupendous survival act. It will still take some doing, but the fixture list has at least been kind. Home wins against Norwich, Hull and Crystal Palace could propel Fulham to safety and Magath believes that this victory will deliver crucial confidence ahead of the run-in. If his side can replicate this performance full of enterprise and desire, they might just do it.

The visitors aimed to take advantage of Aston Villa’s frailty and settled far quicker than their hosts. Teenage striker Cauley Woodrow looked lively up front, heading over the bar in Fulham’s first attack, and then nearly capitalised on a shocking mistake for Joe Bennett, beating Nathan Barker to a criminally short pass, and bursting down the inside-right channel only for Brad Guzan to push away his powerful, angled shot. Villa, without the injured Christian Benteke and the sick Gabby Agbonlahor, offered little – with David Stockdale called into action only to save from Leandro Bacuna.

Magath shuffled his pack at half-time, introducing Rodallega and Ashkan Dejagah for Woodrow and the ineffectual Pajtim Kasami. The Iranian winger immediately enlivened proceedings with his willingness to run at the full-back, although Fulham were nearly caught on the break five minutes into the second period, as Bacuna burst into the box and nearly scored – Stockdale turned his fierce drive onto the near post. The Fulham goalkeeper also claimed a drive from Andi Weimann after Grant Holt had cut the ball back nicely for the Austrian, but Fulham attacked with such vigour and belief it was little surprise when they took the lead.

Dejagah drove purposefully at the Villa defence again and this time, with little pressure on the ball, squared it for Kieran Richardson to curl a magnificent finish into the top corner from the edge of the box. The porous nature of Fulham’s defence – comfortably the worst in the top flight – suggested they would be unable to hold onto such a slender advantage and so it proved. Villa were level within seven minutes, through a goal of remarkable simplicity. Holt headed in Marc Albrighton’s corner from twelve yards after Brede Hangeland badly mistimed his jump.

It seemed a familiar story for the bottom club, especially once Matt Lowton had superbly cleared off the line after Lewis Holtby glided around Brad Guzan and stabbed an effort towards goal. The Villa defender scrambled the ball clear, with the goal-line technology showing that only a fraction of the ball hadn’t crossed the line. At the other end, the visitors were indebted to a splendid save from David Stockdale, who turned aside a swerving effort from susbtitute Alexander Tonev that appeared destined for the top corner.

Fulham kept pushing forward and got their reward with four minutes to play. The magnificent Mahamadou Diarra, making his first Premier League appearance for nearly two and a half years, won the ball back after Villa had half cleared a Holtby free-kick and found the German midfielder wide on the right. Holtby’s whipped cross was deftly flicked home by a delighted Rodallega – and Magath’s side managed to withstand four minutes of injury time to hold on to those three precious points.

ASTON VILLA (4-4-1-1): Guzan; Lowton, Bennett (Tonev 66), Vlaar, Baker; Westwood, Bacuna, Albrighton (Bowery 90), Bertrand; Weimann; Holt. Subs (not used): Steer, Clark, Luna, Sylla, Robinson.

BOOKED: Bennett, Westwood, Albrighton.

GOAL: Holt (70).

FULHAM (4-5-1): Stockdale; Heitinga (Riise 83), Richardson, Hangeland, Amorebieta; Diarra, Riether, Sidwell, Holtby, Kasami (Dejagah 45); Woodrow (Rodallega 45). Subs (not used): Stekelenburg, Kvist, Kacaniklic, Roberts.

BOOKED: Sidwell, Holtby.

REFEREE: Michael Oliver (Northumberland).