The Senegal international took advantage of a costly slip by Reds skipper Steven Gerrard to surge clear and coolly beat Simon Mignolet on the stroke of half time.
And the Blues wrapped up the points when one-time Kop hero, Fernando Torres unselfishly laid on a tap-in for Willian in injury-time after the visitors broke clear.
Chelsea made seven changes from the side that drew at Atletico Madrid in the Champions League and looked to disrupt Brendan Rodgers' outfit throughout a game of attack versus defence.
Liverpool went close through Mamadou Sakho but that would be as near as they came as another big-game Jose Mourinho masterclass saw the hosts continually frustrated.
Andre Schurrle almost doubled the lead after the break with a rasping drive that Simon Mignolet did well to parry while at the other end the Reds saw long-range shots from Gerrard and Joe Allen fly wide.
Luis Suarez almost snatched an equaliser when he stung the fingertips of Mark Schwarzer before Willian sealed the triumph.
The result sees Chelsea close the gap on the leaders to two points, while Manchester City can leapfrog Liverpool into top spot on goal difference if they win their two games in hand.
PRE-MATCH: Sturridge on the bench, seven changes for Chelsea. Liverpool named an unchanged team as Sturridge was deemed only fit enough for the bench. As promised Mourinho rang the changes with Tomas Kalas coming into the defence for his Premier League bow.
15' - LIVERPOOL CHANCE! Mamadou Sakho blazes Suarez's drilled ball across goal over the top after Cole had miscued a clearance off the line.
45+3' - CHELSEA CHANCE! A right-wing corner is driven into the area towards Kalas who leaps highest but can't connect.
45+3' - GOAL! Liverpool 0-1 Chelsea. A slip by Gerrard allows Ba to break clear and coolly slip the ball past Mignolet. Huge goal in the title race!
59' - GOOD SAVE! - A clipped ball by Johnson is only cleared towards the edge of the box for Allen who drills in a low volley that Schwarzer pushes away.
61' - BIG SAVE! - Schurrle surges in from the left and smashes in a low shot that Mignolet just about reaches to palm to safety.
90+3' - GOOD SAVE! - A late corner drops to Suarez who sees his thumping effort tipped over by Schwarzer.
90'+4' - GOAL! Liverpool 0-2 Chelsea. The Blues seal victory as Torres and Willian break completely clear with no red shirt in sight. The former Liverpool striker rolls an unselfish pass to Willian who walks it in.
Liverpool failed to score for the first time in 26 league matches.
The Reds lose their first game in 17 outings.
Mourinho has only lost once nine meetings with Liverpool in the Premier League.
Chelsea have still conceded only 15 goals on the road, the fewest of any team in the top four divisions.
Advantage City? If Manchester City win their games in hand they will top the table courtesy of a better goal difference. Have Liverpool blown it? Or can Chelsea sidestep both and land an unlikely title. This one will go to the wire.
MAN OF THE MATCH
Branislav Ivanovic (Chelsea): The defender was superb throughout, helping Kalas to enjoy an accomplished first Premier League start while nullifying everything Liverpool threw at them.
Liverpool: Mignolet 6, Johnson 6, Flanagan 6, Skrtel 6, Sakho 6, Gerrard 6, Allen 6, Lucas 5, Coutinho 6, Sterling 7, Suarez 6. Subs: Sturridge 5, Aspas 5.
Chelsea: Schwarzer 6; Azpilicueta 7, Ivanovic 8, Kalas 7, Cole 7, Lampard 6, Mikel 6, Matic 6, Salah 5, Ba 7, Schurrle 6. Subs: Willian 6, Cahill 6, Torres 6.