The big news before the contest was the inclusion of Reece James, who was thrown straight into the starting lineup for his first competitive appearance of the season.
James made a promising start to proceedings, but his fellow defender Levi Colwill gifted Liverpool the chance to take the lead in the 26th minute, with his clumsy foul giving Mohamed Salah the chance to blast home a 29th-minute penalty.
The Reds briefly thought they had doubled their advantage through Cody Gakpo, only to see the close-range effort ruled out for an offside in the build-up.
From nearly doubling their advantage, Arne Slot's side found themselves on level terms when Nicolas Jackson's 48th-minute effort was awarded after it had initially been ruled out for offside.
However, Liverpool produced an impressive response to Chelsea's equaliser, with Jones latching onto Salah's inch-perfect cross to restore the home side's lead with immediate effect.
The Reds ultimately saw out the remainder of the contest to clinch all three points, moving them back to the top of the table after they had dropped down to second following Manchester City's win over Wolverhampton Wanderers.
While the Reds celebrated a seventh consecutive victory in all competitions, Chelsea are left to reflect upon their first Premier League defeat since losing to Man City on the opening day of the season.
LIVERPOOL VS. CHELSEA HIGHLIGHTS
Salah goal vs. Chelsea (29th min, Liverpool 1-0 Chelsea)
Penalty to Liverpool. The Reds get the chance to go to the spot after Colwill is penalised for a clumsy challenge on Jones. Salah steps up to send Sanchez the wrong way and fires home his fifth Premier League goal of the season.
Gakpo disallowed goal vs. Chelsea (32nd min, Liverpool 1-0 Chelsea)
Gakpo has the ball in the net but the assistant's flag cuts the celebrations short. Replays confirm Salah had taken up an offside position before playing the ball across for Gakpo to tap home from close range.
Jackson goal vs. Liverpool (48th min, Liverpool 1-1 Chelsea)
Chelsea pull level in the opening stages of the second half. Jackson races through on goal before slotting past Caoimhin Kelleher at the near post. A VAR review confirms Ibrahima Konate played Jackson onside after the goal was initially chalked off for offside.
Jones goal vs. Liverpool (51st min, Liverpool 2-1 Chelsea)
Jones restores Liverpool's advantage within three minutes of Chelsea's equaliser. The midfielder makes a run from deep to collect Salah's inswinging cross before prodding past Sanchez to spark scenes of jubilation among the home support.
MAN OF THE MATCH - CURTIS JONES
Salah may have registered a goal and an assist, but Jones ultimately pips him as the standout player in Liverpool's home success.
The midfielder earned the spot-kick for the opener, before he produced the game's decisive moment in the 51st minute.
Jones timed his run to perfection to receive Salah's inviting delivery and then showed great composure to poke the ball past Sanchez.
Overall, he won the majority of his duels, created a couple of chances and made 90% of his 41 passes to help Liverpool clinch all three points.
LIVERPOOL VS. CHELSEA MATCH STATS
Possession: Liverpool 43%-57% Chelsea
Shots: Liverpool 8-12 Chelsea
Shots on target: Liverpool 5-2 Chelsea
Corners: Liverpool 1-5 Chelsea
Fouls: Liverpool 10-12 Chelsea
BEST STATS
WHAT NEXT?
After claiming three precious points, Liverpool will now head to Germany for Wednesday's Champions League meeting with RB Leipzig, before they face Arsenal in next weekend's mammoth Premier League clash.
As for Chelsea, they will travel to Greece for Thursday's Conference League game against Panathinaikos, before they play host to Newcastle United next summer.