The Reds showed no sign of fatigue after winning the Club World Cup in Qatar last weekend, with their nearest challengers Leicester overwhelmed at the King Power Stadium.
Former Liverpool boss Brendan Rodgers saw his side fall behind to Firmino's first-half header before Jurgen Klopp's men scored three times in seven second-half minutes.
BOBBY FIRMINO 🤩 pic.twitter.com/BF520ucgS5— NBC Sports Soccer (@NBCSportsSoccer) December 26, 2019
Substitute James Milner made it 2-0 from the penalty spot before Alexander-Arnold teed up Firmino for his second and then finished the scoring himself as Liverpool moved closer to a long-awaited title.
James Milner is cooler than cool ❄️ pic.twitter.com/nImNz7p8Ok— NBC Sports Soccer (@NBCSportsSoccer) December 26, 2019
After a pre-match build up that featured fireworks and flashing lights, Leicester looked completely overawed by the occasion and almost conceded twice in the opening 70 seconds.
Kasper Schmeichel denied Alexander-Arnold's effort from range before Sadio Mane lost Jonny Evans but miscued his attempt from Mohamed Salah's cross.
The Foxes continued to roll the dice, Evans' misplaced pass resulting in another chance for Salah, who was just pushed too wide after Schmeichel rushed out and failed to get near the Liverpool forward.
Wilfred Ndidi was the next to lose possession, recovering to deflect Jordan Henderson's effort wide, before the leaders finally made the breakthrough.
Alexander-Arnold whipped an inviting ball from the left to the back post and Firmino guided his header between Schmeichel's foot and the post.
Schmeichel rescued Evans by denying Mane following another error from the Northern Irishman, with Leicester fortunate to only be trailing by one goal at the break.
Liverpool were relentless after the resumption too, though Firmino side-footed Andy Robertson's delivery wide after Dennis Praet became the latest man in a blue shirt to be dispossessed.
It did not matter as a seven-minute blitz saw the Reds put the game to bed.
First Caglar Soyuncu leant into a corner and the ball struck his arm, with referee Michael Oliver pointing straight to the spot, from where Milner coolly dispatched the penalty.
Firmino then turned home another cross from Alexander-Arnold, who finished past Schmeichel himself to give Liverpool a fourth goal en route to their 17th win out of 18 Premier League games this season.
Alexander-Arnold is unreal, Liverpool call game 😤 pic.twitter.com/7Tz8UQoXKW— NBC Sports Soccer (@NBCSportsSoccer) December 26, 2019
It's only fitting that Trent gets his goal ⭐️ pic.twitter.com/i9uTYeELye— NBC Sports Soccer (@NBCSportsSoccer) December 26, 2019
What does it mean? Title firmly in Liverpool's sights
Klopp's side were 10 points clear at Christmas, an advantage only one side - Newcastle United in 1995-96 - had failed to convert into a title triumph. Even if Manchester City reduce the 13 point-gap to 11 on Friday, the Reds have a huge lead at the season's halfway stage.
Leicester had looked like their most likely challengers but back-to-back defeats against City and Liverpool suggest another title bid looks unlikely.
More assists, and a goal, for Alexander-Arnold
No player has provided more Premier League assists since the start of last season than Alexander-Arnold, who moved onto 20 with a couple here.
Furthermore, the right-back got in on the act himself with the fourth goal, having impressed defensively too.
Soyuncu hands Liverpool crucial second goal
There were plenty of poor performers among the Foxes, including James Maddison, the largely anonymous Jamie Vardy and Evans, but Soyuncu sealed the game for the Reds.
He left referee Oliver with no choice when he needlessly leant into the corner, and Milner made him pay.
Leicester travel to West Ham on Saturday while Liverpool round off a memorable 2019 against Wolves on Sunday.