Striker Ba broke the deadlock just before break, while Willian added a second deep into stoppage time as the West Londoners moved to within two points of their hosts.
Here, Sports Mole has looked back over the contest to determine if the result was a fair one.
On target: 8
On target: 4
Was the result fair?
The statistics above show that Liverpool did indeed dominate large parts of the contest, yet of their 26 attempts, there were not too many that caused Chelsea goalkeeper Mark Schwarzer to break into a sweat. The Blues came with a gameplan and they executed it to perfection. For that reason, you would have to say that Chelsea were deserving victors.
In recent weeks Liverpool have scored early goals, which has meant that neither the players nor the fans have had a reason to grow nervous. What's more, they also haven't required a Plan B, because the likes of Raheem Sterling, Luis Suarez and Philippe Coutinho have torn teams apart.
It was clear very early on today, though, that Plan A wasn't going to work - Chelsea were too resolute. As a result, Suarez was often isolated up front, even with the second-half introduction of Daniel Sturridge. For all their domination, Liverpool never truly gave the impression that they were going to score, in stark contrast to their other outings of late.
Say what you like about Jose Mourinho and the somewhat negative tactics that he sometimes deploys in big matches, but it gets the job done. His side was missing some key personnel, which in turn resulted in a debut for young Tomas Kalas in defence. Despite the changes, every member of the starting lineup knew his role and carried out their orders to the letter.
Then, when the chances did arise to go forward, they caused a couple of problems, as well as scoring at key moments. A goal at the end of either half gave Liverpool no time to respond.
Sports Mole's man of the match
Tomas Kalas: The 20-year-old had never started a Premier League game before today, but by the time that the final whistle was blown, he looked a veteran. Alongside Branislav Ivanovic, Kalas was charged with the task of frustrating the 30-goal Suarez. Many centre-backs have tried to do that this year, but few have done a better job than the youngster from the Czech Republic.
Having done so much to get Liverpool to the top of the league, an error from their captain Steven Gerrard could end up proving pivotal in costing them a first title in 24 years. Just inside his own half, the Liverpool skipper allowed the ball to roll under his foot and as he tried to atone, he slipped. That presented the chance for Ba to run through on goal, before he slotted in the game's opening goal.
Martin Atkinson was always likely to be a busy man and so it was proved. He did get the occasional call wrong, such as the decision to award Liverpool a corner when Gerrard had clearly skewed the ball out of play late on, but it was a steady display from the match official.
Liverpool: The Reds will look to return to winning ways away at Crystal Palace next Monday night.
Chelsea: As for Chelsea, they will play host to struggling Norwich City a day earlier.