Manchester City defeated Leeds 4-0 to maintain their one-point lead over Liverpool in Premier League.
Burnley won for the first time since Sean Dyche's sacking thanks to Connor Roberts' sublime curler and Nathan Collins' header.
The 50-year-old Dyche, who signed a new contract due to run until 2025 in September, had been the longest-serving manager of any club in the Premier League, having taken charge in October 2012.
Frank Lampard's team tumbled to within a point of the relegation zone after conceding in the 85th minute to lose 3-2 at Burnley in a wild, end-to-end match on Wednesday.
City and Liverpool are locked in a thrilling shootout at the top of the English top flight, with just eight matches remaining of the season.
Chelsea scored four goals in a 21-minute burst at the start of the second half in a 4-0 win at Burnley in the English Premier League on Saturday.
Brendan Rodgers' side stole the points with two goals in the last eight minutes as Vardy set up James Maddison and then netted himself.
Liverpool have won their last nine games in all competitions, with none more important than this success in their game in hand on City.
City's lead at the top is down to six points after a pulsating afternoon that could serve as a seismic shift in the Premier League's battle for supremacy.
Fabinho struck late in the first half at windswept Turf Moor to give Liverpool their fourth successive league victory.
Premier League: Manchester United frustrated in Burnley draw; Newcastle boost survival bid with win over Everton
Ralf Rangnick's side slipped down to fifth place after Jay Rodriguez cancelled out Paul Pogba's opener at Turf Moor.
The striker, who is 6 feet 6 inches (1.98 metres) tall, has signed a three-and-a-half-year contract at the club, who are bottom of the Premier League with just one win in 18 games this season.
Liverpool kept hope of a title race alive as a 3-1 win over Crystal Palace cut the gap on leaders Manchester City to nine points.
The 30-year-old, who has signed a two-and-a-half year contract, has moved to St James' Park for an undisclosed fee, which reports said was £25 million ($34 million).
Covid-19 cases within the Everton camp had seen the Merseysiders request a postponement on Thursday.
A total of 12 matches have now been called off in the past two weeks as Britain battles record numbers of positive Covid cases due to the Omicron variant of the virus.
Just four games are now due to be played this weekend, with Leeds against Arsenal the only surviving fixture on Saturday.
Premier League: Arsenal thrive despite Pierre-Emerick Aubameyang row as league's Covid crisis deepens
Arsenal are one point above fifth-placed West Ham after a second successive victory eased the drama surrounding Mikel Arteta's decision to strip Gabon forward Aubameyang of the club captaincy.
Leicester left Newcastle still rooted in the Premier League relegation zone with a 4-0 victory, while Palace's 3-1 win against slumping Everton piled the pressure on Rafael Benitez
Chelsea extended their lead at the top to three points as Reece James scored twice in a 3-0 win at Newcastle.