In their first League match since the announcement that Jurgen Klopp will leave the club at the end of the season, Liverpool needed to respond after Arsenal's victory over Nottingham Forest on Tuesday night briefly closed the gap.
It was clear almost from the first whistle that the Reds would do just that, as they pinned Chelsea back and swarmed all over a creaking defence.
Darwin Nunez hit the woodwork twice early on in a typically all-action display, and Liverpool's deserved opener inevitably came midway through the first-half. Bradley, sensational throughout, played the ball inside, and Diogo Jota bundled his way through the defence before finishing from close range.
Bradley got a goal for himself, his first for the club, as Luis Diaz slid the ball through to the right-back and he drove into the box, firing a superb strike into the far corner.
The match should have been put to bed in first-half stoppage-time, but Nunez instead brought up an unwanted hat-trick. Jota was brought down in the box and the Uruguayan stepped up to take the penalty, but smacked his spot-kick off the post, the third time the woodwork had denied him.
Liverpool's third goal did come, 20 minutes into the second-half, and Bradley again played a leading role. He whipped in a superb cross and Dominik Szoboszlai powered home a header to seemingly put the result beyond doubt.
But Christopher Nkunku, off the bench, gave Chelsea hope as he pulled one back, dragging an effort in off the post. He should too have had a penalty minutes later after being brought down by Virgil van Dijk, but the referee and VAR waved play on, much to Mauricio Pochettino's bemusement.
The Chelsea boss' mood was not improved when Liverpool moved three goals clear again, Diaz left with a simple finish as Nunez, who had by now hit the woodwork for a fourth time after thundering an effort off the bar, played the ball across the face of goal and the Colombian provided the finishing touch.
Liverpool head to north London this weekend full of confidence for a title showdown with Arsenal, having laid down a marker against Chelsea ahead of next month's rematch with the Blues in the Carabao Cup final.