Jonathan Walters' sixth career goal against Liverpool handed Stoke the lead early on, before goals from Adam Lallana and Roberto Firmino swung the game in the hosts' favour before half-time.
A second-half stroll saw Giannelli Imbula turn into his own net from Divock Origi's low cross on the hour before Daniel Sturridge scored the fourth less than a minute after coming off the bench, rounding Lee Grant and scoring with his first touches for his first league goal of the season.
That meant Liverpool leapfrogged Manchester City, whom they face on New Years' Eve at Anfield, back into second in their penultimate game of the calendar year and have now lost just one of their last 16 top-flight matches.
Only one change across two line-ups
Jürgen Klopp named an unchanged side for the third successive game after wins away at Middlesbrough and Everton prior to Christmas, a first for the German after 14 months in charge.
That meant Simon Mignolet was still preferred over Loris Karius in goal, with Ragnar Klavan filling in for the absent Joel Matip in the heart of defence.
Striker Daniel Sturridge remained on the bench despite his contributions in the dramatic late Merseyside derby win last Monday.
Stoke manager Mark Hughes meanwhile handed 35-year-old striker Peter Crouch his first start in exactly four months with his only change from a 2-2 draw with Leicester City when they had led 2-0 against 10 men until the 74th minute.
Former Liverpool striker Crouch, who scored 42 goals in 134 appearances as a Liverpool player, replaced Bojan as one of three former Reds in Stoke's starting line-up, added to Glen Johnson and Joe Allen - who only moved to the Potteries in the summer.
With Marko Arnautovic serving the second game of his three-match suspension, Ibrahim Afellay made the bench as he looked to make his first appearance since April after being sidelined with knee ligament damage.
Stoke break the deadlock against run of play
Liverpool's remarkable improvement on home soil under Klopp has been underlined by their 15-game unbeaten run at home in the Premier League, the longest such stretch of any team in the division.
And there were glimpses of the free-flowing, attacking football that has become synonymous with their performances on L4 this season as they started the stronger side in the first 10 minutes.
Only inches separated them from early opportunities, Divock Origi and Sadio Mane fizzing crosses just out of the reach of Georginio Wijnaldum and Firmino, while Jordan Henderson curled over the crossbar from the edge of the area.
But despite being second-best early on, it was Stoke who hit the front on 12 minutes after a couple of instances of the Potters' aerial threat through Crouch.
Liverpool failed to clear their lines after a Crouch header was blocked, Mane tracking back to beat Erik Pieters to a dropping ball before inexplicably switching off and allowing the left wing-back to find space on the outside and swing a cross into the near post.
There, Walters arrived ahead of Dejan Lovren to direct a header past Mignolet, despite the Belgian getting a good hand to the ball with his outstretched right, to make it 1-0.
As a result, Klopp's charges had conceded the first goal in a home game for the first time this season and were in an unfamiliar position, the pressure firmly on after their close rivals' respective wins the previous day.
The Reds looked to muster a response but should have gone 2-0 down, Mignolet getting down low to deny the returning Allen with a strong right hand. They were fortunate the rebound narrowly evaded Crouch before Klavan blocked Pieters' follow-up.
Reds score two in 10 minutes to go into half-time in front
Liverpool's defensive uncertainty and their threat going forward, coupled with Stoke's increasing confidence, made for an engaging 20 minute spell - though not for 50,000 home supporters fraught with nerves and worries of another setback.
Stoke's intent to frustrate worked well, Crouch clearing Firmino's drive off the line after a corner as the visitors continued to enjoy the better of the game. Their high balls, and the width provided by their wing-backs, caused a multitude of problems.
Yet Liverpool relieved themselves of growing tension with a much-needed equaliser when Adam Lallana squeezed beyond Lee Grant from a tight angle on 34 minutes.
Mane found space down the right after Origi's ball out wide and though Lallana couldn't control the winger's cross, the ball bounced back off Johnson and fell kindly for Lallana - who fired low between Grant and the near post from a tight angle for his seventh of the campaign.
That transformed the atmosphere and attitude among the supporters and the players and Firmino went close when he swept over the bar from Lallana's pull-back.
But Liverpool reversed the scoreline in ideal time when Firmino struck his first goal in seven games and his 15th of the calendar year, spinning towards goal and firing a right-footed effort which came off the inside of both posts before crossing the line.
And they almost added to their lead as Mane saw a deflected first-time effort bobble wide of Grant's far post.
Own goal adds comfort to hosts' advantage
But after a scrappy first 15 minutes of the second-half, Liverpool extended their winning margin to two to give themselves the kind of comfort they had lacked all evening.
Origi burst away into space down the left, delivering a low cross that Imbula - in his attempt to prevent Mane from scoring - poked into his own net for 3-1.
From there onwards, Liverpool applied the guile and class that has encapsulated some of their previous Anfield performances - Mane nearly claiming a goal of his own only for his shot to once again trickle wide due to a deflection.
That goal ensured Liverpool have scored more league goals in 2016 than any year since 1989 with 85, an astounding 44 coming in the 18 games of this season alone.
And they looked like adding to that as they inflicted more pain to Stoke's miserable run at Anfield, the Staffordshire-based side having gone 32 games without a win in the league here - their last victory coming in March 1959.
Sturridge's instant impact adds further gloss
Liverpool did just that through Daniel Sturridge on 70 minutes, the striker scoring just 54 seconds after entering the field of play. Stoke skipper Ryan Shawcross tried to play back to Grant without looking, but only played through the lurking Sturridge and he netted his first Premier League goal since April, rounding the 'keeper and sliding in.
That, on a night filled with goalscoring statistics, delivered Liverpool's 100th league goal under Klopp and recreated the 4-1 scoreline that they managed at home to Stoke last season. It was also their 86th of 2016 and their 45th of this season alone.
It looked like it would only get worse for Stoke, Firmino somehow failing to turn in from Lovren's first-time square ball, before midfielder Afellay was introduced to make his comeback from a lengthy injury.
And fellow substitute Alberto Moreno went close with an acrobatic effort after Sturridge failed to turn Henderson's tame shot towards goal and the ball bounced up for the Spaniard to try the spectacular.
Yet despite controlling proceedings, Liverpool couldn't build on their three-goal advantage. Though they won't have minded all that much as they returned to second, six points behind front-runners Chelsea, with another emphatic example of their title credentials.