Jurgen Klopp's side is now a whopping 16 points ahead of second-place Leicester City, which lost to Southampton earlier in the day, although its lead at the summit could be cut to 14 points if Manchester City overcomes Aston Villa on Monday (AEDT).
The Reds were dominant in the first half and made the most of their superiority when Firmino expertly drilled home from inside the penalty area after 37 minutes.
Son Hueng-min and Giovani Lo Celso squandered golden opportunities to snatch a scarcely deserved point for Jose Mourinho's men late on, with Liverpool ultimately holding on for yet another three points.
Liverpool twice came agonisingly close to going ahead inside two minutes. Firmino's initial effort was cleared off the line by top-flight debutant Japhet Tanganga, with Alex Oxlade-Chamberlain lashing against the post from the follow-up.
Lucas Moura, Son and Dele Alli all missed the target from promising positions soon after, while at the other end Virgil van Dijk headed straight at Paulo Gazzaniga from just six yards.
There was little the Spurs goalkeeper could do to deny Firmino eight minutes before the interval, the Brazil international controlling Mohamed Salah's pass with a sublime touch before lashing in from 10 yards.
Spurs started the second half with a spring in their step and twice came close before the hour mark, with Serge Aurier testing Alisson and Son seeing an effort deflected narrowly wide.
The game was almost put out of reach in the 66th minute but Gazzaniga got down sharply to paw away Sadio Mane's header.
Spurs rallied in the closing stages, with Son blazing over from a glorious position and substitute Lo Celso somehow diverting Aurier's cross wide from inside the six-yard box seven minutes from time.
Klopp was visibly furious at his side's defending, but it mattered little in the end as it held on for a win that strengthens its already formidable position at the summit.