Chelsea midfielder Jorginho missed his first penalty for the club on the same afternoon he made his 100th appearance for the Blues.
Frank Lampard's side went down two goals against the defending champions on Sunday as a pair of disastrous mistakes proved costly.
Andreas Christensen put his side in serious trouble with a red card just before half-time, with Sadio Mane then opening the scoring five minutes after the break.
Mane then added his second just minutes later as under-fire Chelsea goalkeeper Kepa Arrizabalaga played an awful pass directly to the forward, who calmly slotted home into an empty net.
The home side, though, were given a chance to get back into the match with 15 minutes to play after Liverpool debutant Thiago Alcantara fouled Timo Werner in the box.
Jorginho stepped up to the spot, having converted all eight of his previous penalty attempts with the Blues.
However, the Italy international's ninth try proved to be a different story as Liverpool goalkeeper Alisson came up with the save to preserve his side's two-goal lead.
Chelsea had been on a streak of 16 consecutive scored penalties in the Premier League, with their last miss coming when Eden Hazard failed to score against Manchester City in April 2017.
It was also the first time that Alisson had saved a penalty for Liverpool, with the Brazilian having conceded on all three previous attempts.
1 - Jorginho has missed a penalty for the first time in nine attempts for Chelsea in all competitions, while this was Alisson's first penalty save for Liverpool since joining the club (three faced). Reach. pic.twitter.com/lgo1uhSyqf— OptaJoe (@OptaJoe) September 20, 2020
In fact, the save from Alisson was his first of the season after the goalkeeper conceded three goals against Leeds in Liverpool's 4-3 opening-day win at Anfield.
Jorginho's penalty miss all but ended Chelsea's chances of getting anything from the match, as Liverpool cruised to a 2-0 win at Stamford Bridge.
The win marked the first time the reigning league champions had won away at Chelsea in the Premier League since Manchester United pulled off the feat in April 2002, with the Blues unbeaten in 13 such matches (seven wins, six draws) before Sunday.
It was also just the third time Chelsea had lost their first home match of a Premier League season after they also did so against Blackburn in 1993-94 and Burnley in 2017-18.