In the streets surrounding Selhurst Park one slogan proudly advertises the club's philosophy: "Tomorrow's players, today". On Saturday afternoon one such youthful talent lived up to that boast, standing tall among the rest, a Palace academy product and England U-21 international, 19-year-old Wilfried Zaha scored his second double of the week to help convert a 2-0 deficit to an emphatic win for his side.

With Palace now unbeaten in seven matches you could add manager Dougie Freedman's name to that billing. The 38-year-old spent 12 of his 16 years at the club as a player before being appointed manager just over 18 months ago and has turned around the club's fortunes — from relegation zone fodder to play-off contenders who are fourth in the Championship. Ironically it was his opposite number, the Burnley manager, Eddie Howe, who had been the Palace chairman Steve Parish's original target for the job. How Parish must thank his lucky stars he got Freedman instead.

Palace's sixth victory in seven games echoed the 3-2 result over Cardiff just a fortnight ago when the home side had performed a similar miracle to return from a 2-0 deficit at half-time. "It's three different games where we've had to come back," Freedman said. "I felt they scored two goals against the run of play that put us on the back foot but I felt the response from the lads and that little bit of quality up top won us the game. In the second half there was only going to be one winner."

Still, going 2-0 down stunned the 21,000 strong crowd into silence, as the in-form side took an early battering from a team in the bottom half of the table. The visitors' lead came as Chris McCann scored from inside the six-yard box. Just three minutes later and Martin Paterson sent in a looping, speculative ball, whirling away to celebrate in delight as it dropped down neatly into the back of the net.

But a brilliant response from Zaha, last season's Football League Young Player of the Year, halved the deficit. The Ivory Coast-born striker latched on to a perfect cross from André Moritz before combining skill and pace to expertly nip in front of the defender Kieran Trippier and slot home. The relief and jubilation raised the noise levels around the ground as supporters sang, "He's just too good for you".

It was the home side who emerged the more fired up after the break. Zaha and Moritz combined well to put pressure on the Burnley defence and eight minutes into the second half their efforts paid off with the equaliser. Another assist from the Brazilian set up Zaha, as the teenager powered into the area and nutmegged the Burnley goalkeeper, Lee Grant, for a smooth finish.

Damien Delaney secured the third, and vital, goal. But it was Glenn Murray's strike that sealed the victory, played in by Dean Moxey after a pass from the substitute Jonathan Parr – on for the teenager Jonny Williams who had been subbed on and then off with an injury after 10 minutes of action.

Burnley were not quite finished yet though and their top scorer, Charlie Austin, made use of a defensive error to tap in his 15th goal of the season.

Howe talked about "suicidal defending" as his side dropped points from a lead for a third successive game. "Hugely disappointed to lose the game when you're scoring as many goals as we are at the moment and we're not getting the points," he said of his team who are the league's top scorers. "It's hugely frustrating. We feel very low tonight."

The mood in the Palace dressing room was not entirely dissimilar according to Delaney, who described the team as "sombre", a fact that he welcomed. "If you're a little bit down after winning 4-3 and going fourth in the league you must be doing something right."

The centre-back said that the team did not panic – even at 2-0 down – a fact that he attributed largely to Zaha, whom he hailed as the best player in the division.