Cesc Fabregas had given the hosts a fifth-minute lead but the Eagles hit back and turned the game on it's head within six minutes.
Wilfried Zaha finished a fine solo run with a smart finish before setting up Christian Benteke for a dinked effort.
Giuseppe Murro was at Stamford Bridge is assess the key Crystal Palace talking points...
Palace are in a hurry to get safe under Allardyce
This result at Stamford Bridge means it is now four straight wins and Palace are four points clear of the relegation zone.
Palace were excellent all over the pitch and look a different team to the one that was struggling so badly a month ago.
The decision to bring in Allardyce to keep them up looks like a brilliant one.
Defensive training paying dividends
Allardyce has done endless defensive drills with his players since taking over and Palace defended for their lives against Chelsea.
Chelsea had wave after wave of attacks but Palace repelled whatever the leaders through at them.
Allardyce has made his mark.
Zaha becoming one of the Premier League's best
Gareth Southgate will be rueing the winger's decision to chose Ivory Coast before England.
Zaha has been in the spotlight in recent weeks and the decision by England managers to overlook him in the past is looking like a mistake.
Zaha scored a brilliant individual goal for Ivory Coast against Russia last Friday and again impressed here.
Benteke finally shows how important he can be
Benteke has struggled since Allardyce took over at Selhurst Park and said this week that Allardyce’s defensive style of football is the reason behind his lack of goals.
The forward had scored just once in 11 games under Allardyce before today but scored and led the line excellently at Stamford Bridge.
Hennessey will not have a better game this season
The Palace goalkeeper was outstanding against Chelsea and made countless saves to frustrate Chelsea and open up the title race.
The ball was like a magnet to Hennessey at times as Palace recorded an unlikely win.
Mamadou Sakho was also a rock at the back