Jose Mourinho's men lost 3-1 to Everton in the lunchtime kickoff with Steven Naismith coming off the bench to score a stunning hat-trick at Goodison, while in the evening feature match Manchester United's record teenage signing Anthony Martial scored a brilliant individual goal on his debut as a second half replacement.
Martial, who has been compared to fellow Frenchman Thierry Henry, cut through the Liverpool defense to score the clinching goal in a 3-1 win for Louis van Gaal's team.
Naismith had struck twice in five pulsating first minutes to leave Chelsea reeling as it looked to recover from a poor start to its EPL campaign
Nemanja Matic gave Chelsea hope with a superb strike just before halftime, but after surviving prolonged visiting pressure, Everton wrapped up the three points when Naismith completed his hat-trick near the end.
The result left Chelsea with just four points, trailing leader Manchester City by 11 points, but not for the first time Mourinho was convinced his team had suffered an injustice.
'We deserved better and played for a better result,' he told the club's official website.
'The biggest concern is that everything goes against us. We know we are making mistakes but with every mistake we are punished immediately. "
Chelsea's day got worse when Manchester City took full advantage with a last-gasp victory at Crystal Palace.
City lost Sergio Aguero to a worrying injury but Nigerian teenager Kelechi Iheanacho came on as a late substitute to score an 89th minute winner.
He reacted quickly after Alex McCarthy saved from Samir Nasri to keep City's 100 per cent start to the season.
Manager Manuel Pellegrino praised his match winner. "Kelechi is a very important striker and just 18 years of age. He has a lot to improve," he told Sky Sports.
Fellow title challenger Arsenal also boosted its challenge with a 2-0 home win over Stoke.
Goals from Theo Walcott and Olivier Giroud in either half gave the Gunners its first home victory of the season in the league.
United's later victory over its bitter North-west rival Liverpool at Old Trafford was also marked by the first appearance of the season by David de Gea after his transfer to Real Madrid collapsed.
But it will be remembered for Martial's wonder goal, coming almost immediately after Christian Benteke had pulled the visitors back into the game at 2-1 with a stunning volley.
Van Gaal was delighted with the 19-year-old's debut: "When you make a goal like Anthony you cannot wish for more I think," he said.
"A lot of players have made a debut and scored with me so it's a good signal."
After a tepid first half, man of the match Daley Blind scored the opener after a well-worked free kick and the game looked over when Ander Herrera was pulled down and scored from the subsequent penalty.
The win leaves United in second spot, ahead on goal difference of Arsenal, but five points adrift of its city neighbor.