A depleted Blues side earned a famous win at Anfield to end the Reds' 11-game winning streak and breathe life into the club's own hopes of winning the Premier League.
Gerrard's slip on the stroke of halftime allowed Ba to race through unopposed on Simon Mignolet's goal and slot the ball home to give the visiting side a lead it never relinquished.
Liverpool poured forward but was repeatedly frustrated by Chelsea's massed defensive ranks and ran out of ideas long before Willian sprinted up field to tap a second into an empty net at the death.
Brendan Rodgers' men are now just two points clear of Chelsea at the top of the table, while the result also provides a huge boost to third-placed Manchester City's hopes of catching Liverpool.
Much was made before the game of Jose Mourinho's team selection three days ahead of the second leg of Chelsea's Champions League semifinal against Atletico Madrid.
The Portuguese had hinted at fielding a weakened side and did just that on Sunday, leaving Gary Cahill and Willian on the bench and handing a Premier League debut to 20-year-old defender Tomas Kalas.
With Frank Lampard, John Obi Mikel and Nemanja Matic - all unavailable for the game with Atletico - screening the back four, Chelsea was set up with the objective of frustrating its opponent and the gameplan worked perfectly as Liverpool struggled to create any clear-cut opportunities, despite enjoying a greater share of possession.
As a result, the league leader drew a blank for the first time in 26 league games and was condemned to its maiden top-flight defeat in 2014, having last been beaten in December's reverse meeting with Chelsea.
Ashley Cole fired an early warning shot for the visiting team in the sixth minute, with a fizzing 25-yard effort that Mignolet parried away low to his left, while Philippe Coutinho volleyed into the side-netting from a tight angle at the other end.
Cole was involved again in the 14th minute, this time clearing off the line after the ball had ricocheted off Mikel, before Sakho scooped Luis Suarez's driven ball over the crossbar from six yards out.
The home side continued to enjoy the greater share of possession and Suarez curled an effort a yard over the bar from the edge of the box four minutes before the interval.
For all Liverpool's dominance, the club fell behind in the third minute of stoppage time at the end of the first half.
Moments after Kalas had glanced a free header wide from a corner, Gerrard's slip allowed Ba to race clear and the Senegalese striker kept his cool to slot underneath Mignolet.
Liverpool tested Mark Schwarzer for the first time in the 59th minute, the Australian getting down low to his left to keep out Joe Allen's first-time volley from just outside the area.
Andre Schurrle brought a similar stop out of Mignolet three minutes later, while Gerrard saw an effort from distance comfortably held by Schwarzer.
Liverpool continued to press hard for an equalizer, Schwarzer tipping Suarez's rasping drive over the bar in stoppage time, but as the home team pushed on it was left exposed at the back and Willian had the simple task of finding an empty net after Torres' unselfish square ball.