Earlier, Liverpool huffed and puffed, but it was Chelsea which went closest before Ba's effort. Ashley Cole forced Mignolet into an impressive save after spectacular drive before Tomas Kalas, on debut, was left kicking the post in frustration after failing to connect with a free header from a Cesar Azpilicueta corner.
Mohamed Salah also had good shout for a Blues penalty, when his goal-bound shot struck Jon Flanagan's hand.
After the break, Liverpool showed more purpose, but found Mark Schwarzer at his best in the Blues goal. The Aussie saved superbly from a Joe Allen volley and denied the Welshman again at the far post.
Gerrard was denied on multiple occasions by Schwarzer, who also saved strongly to parry Luis Suarez's strike late on.
Then Chelsea wrapped up the points in injury time as substitute Fernando Torres found himself clear before setting up Willian for a one-two around Mignolet ahead of the Brazilian tapping into the empty net.