Mauricio Pochettino’s side, bogged down in mid-table, took an early lead through Mykhailo Mudryk but Michael Olise pegged the hosts back at Stamford Bridge.
Madueke won and converted an 89th-minute penalty to claim victory for stuttering Chelsea after three losses in their previous four top-flight matches.
Chelsea owner Todd Boehly has spent lavishly across the past three transfer windows but the Blues have suffered 19 league defeats in the calendar year.
Defeat leaves Palace dangling three points above the relegation zone and coach Roy Hodgson under pressure.
Chelsea dominated the first half and created several openings despite missing suspended attacking pair Raheem Sterling and Cole Palmer, both booked in an error-strewn defeat by Wolves on Christmas Eve.
Pochettino handed left-back Ian Maatsen his first top-flight start on the right of the attack and the 21-year-old came close early on, nudging past Dean Henderson but Tyrick Mitchell cleared the ball away as it rolled towards goal.
Mudryk broke the deadlock in the 13th minute after Christopher Nkunku played in Malo Gusto, zipping outside him on the left.
Gusto squared for Mudryk to slot home for his third league goal of the season.
The Ukraine winger could have added his fourth soon afterwards when Nicholas Jackson teed him up with a brilliant backheel, but Henderson rushed out to save well.
Jackson set up Nkunku, making his first start for the club, but the French forward air-kicked under pressure from Chris Richards.
The hosts were rampant but Palace snatched an equaliser just before the break through Olise after another Chelsea defensive error.
The Blues defence inexcusably left the winger unmarked and he took Jordan Ayew’s cross on his chest superbly before smashing home at the near post.
Chelsea’s initial spark faded and the visitors set up camp in their half, aiming to end a seven-game winless streak.
Playmaker Eberechi Eze whipped a free-kick wide in front of Palace’s baying fans and Chelsea goalkeeper Djordje Petrovic thwarted Jean-Philippe Mateta.
Jackson blew a golden opportunity by firing wide after Conor Gallagher slipped him in, and when he did find the net minutes later the goal was ruled out by VAR for offside.
Chelsea fans were infuriated but their rage turned to cheers when they were awarded a penalty after another video review following Eze’s foul on Madueke.
The 21-year-old winger calmly stroked the ball home and Chelsea held on through Palace pressure in stoppage time to claim a tense victory.
AFP
