Ba's opener came just before the break when Gerrard slipped following Mamadou Sakho's pass. Ba latched onto the ball and ran at goal before nutmegging the advancing Simon Mignolet.
In the second period, Mark Schwarzer made a great save from Joe Allen, while at the other end, Mignolet denied an effort from Andre Schurrle.
Willian then made sure of the win after a pass from fellow substitute Fernando Torres for a breakaway goal in injury time.
The victory saw the second-placed Blues halt Liverpool's 11-match league winning run and move to within two points of their opponents at the top with Manchester City also in a position to take advantage as the title race looks set to go right to the wire.
Chelsea manager Jose Mourinho got his tactics spot on to keep alive his side's hopes of an unlikely double.
In a battle between a home side committed to attack and visitors intent only on defending, the latter triumphed, which may not have made for a good spectacle, but Chelsea - and City - were not complaining.
The Champions League is still the primary objective for the Londoners and to that end they fielded a slightly weaker side, with seven changes from the midweek goalless semi-final first-leg draw at Atletico Madrid, but it still boasted more than 500 international caps with a entire squad value of about £200million.
Tomas Kalas, with just two minutes' action in two different competitions this season, made his Premier League debut at centre-back and coped well.
In January Mourinho criticised West Ham for playing a game from the "19th Century", but the Portuguese brought to Merseyside his own unique brand of defensive football as they slowed the game at every opportunity.
In time-wasting and breaking up play, Chelsea denied their opponents any opportunity to establish the sort of rhythm which has regularly blown away teams in the first half.
It was a classic Mourinho destruction and frustration ploy and infuriated Liverpool so much Gerrard engaged in a bit of push and shove with the Chelsea boss in trying to get the ball back into play and Luis Suarez stood to applaud goalkeeper Mark Schwarzer's time-wasting.
Referee Martin Atkinson made a big show of pointing to his watch, intimating he was adding on time, but he did not take decisive action in actually booking anyone until stoppage time.
Ashley Cole had an early shot parried away by goalkeeper Mignolet but Chelsea were happy to concede possession and territory.
A rehearsed corner saw Glen Johnson's shot deflected behind and Philippe Coutinho volleyed Suarez's cross into the side-netting before Cole cleared off the line from team-mate John Obi Mikel's deflection and Sakho blazed over from the breakdown.
Optimistic shouts for handball against Jon Flanagan were waved away, while, at the other end, Suarez failed to capitalise on Cole's mistake in giving away possession by curling a shot over.
Ba was not as wasteful when Gerrard slipped in possession and he finished expertly.
After the break, Schwarzer produced a great save to keep out Allen's first-time effort, although Mignolet's denial of Schurrle was equally as good.
Gerrard tried his best to redress the balance, but twice found Schwarzer with shots from outside the area and once from a header inside it.
Even the return of striker Daniel Sturridge from a hamstring injury as a second-half substitute did not puncture a hole in Chelsea's thick blue line.
Suarez had one last chance in added time, but Schwarzer punched over his volley before the match ended with the familiar sight of a jubilant Mourinho running down the touchline to celebrate substitute Willian's breakaway goal.