The 33-year-old, who has suffered a dip in form recently, then fired Newcastle's second penalty wide and once keeper Djordje Petrovic saved Matt Ritchie's spot-kick Chelsea had gone from the despair of contemplating defeat to the sheer elation
United keeper David De Gea, making his first appearance of the season after signing a new four-year contract following the breakdown of his move to Real Madrid, demonstrated his worth with fine saves from Danny Ings and Jordon Ibe.
French centre-back Badiashile, making his first start for Chelsea since May, opened the scoring on the half-hour mark after Rovers keeper Leopold Wahlstedt palmed Conor Gallagher's cross from a short corner straight to him inside the area.
The dominant visitors had a strong penalty appeal turned down after Sanchez looked to have been brought down before Jermain Defoe equalised from the spot after keeper Petr Cech had fouled Duncan Watmore.
Samuel Chukwueze clinically dispatched Simon Moses' inch perfect pass beyond thekeeper to break the deadlock. Young striker Taiwo Awoniyi doubled the Super Eagles' advantage on the stroke of half time with an instinctive header.
The Argentine keeper made three superb saves. He twice denied Spanish forward Ferran Torres, pushing one effort wide of the post in the first half before blocking a spectacular overhead kick after the break.
Antoine Griezmann hit the bar for Barca from a tight angle and missed a glorious chance when he tried to slide the ball into an empty net but deflected it to thekeeper.
But Chelsea got the break they needed in a tense finale when the VAR spotted Eberechi Eze had fouled Madueke just inside the area and the substitute expertly sent Palace keeper Dean Henderson the wrong way from the spot.
Thekeeper managed to palm away from his own goalline, but Aubameyang was lurking to pull the loose ball back to Smith Rowe in front of goal, and his low shot squirmed in off the post.
An entertaining encounter looked set to end in stalemate before - with the game entering stoppage time - Firmino soared to flash a header high past Spurs keeper Hugo Lloris from Andrew Robertson's corner.
Jota got his second when he initially miscontrolled, but then recovered his poise to send a low shot beyond the Bournemouth keeper. Uruguay forward Nunez added the fourth in stoppage-time, diverting in Joe Gomez's cross.
England captain Harry Kane, inevitably, was involved with a deft touch to release Kingsley Coman, who easily beat exposed United keeper Andre Onana in front of the Stretford End.
The excellent Eden Hazard curled in a free-kick and Bertrand Traore's header looped over dreadful City keeper Willy Caballero to complete an emphatic win for Chelsea, who were even allowed the luxury of seeing Oscar's penalty saved.
Liverpool missed several first-half chances to put the game to bed, but had to wait until LASK keeper Tobias Lawal felled Gakpo in the area on 48 minutes, allowing Salah to slam in the third, with Gakpo adding a fourth following Trent Alexander-Arnold's