Substitute Roberto Firmino scored with his first touch as Liverpool came from behind to beat struggling Burnley and stay in touch with leaders Manchester City in the Premier League table.
Jack Cork gave the hosts a surprise lead after Alisson could not gather the ball following a corner but Jurgen Klopp's side hit back with three goals.
James Milner equalised with a superb low finish from the edge of the box and Firmino, one of seven players left out from the side that started against Everton on Sunday, tapped home Virgil van Dijk's athletic cutback.
Xherdan Shaqiri made sure of the win for Liverpool with a clinical counter-attack goal moments after Alisson had saved superbly from Ben Mee.
Liverpool are two points behind Pep Guardiola's side after 15 games and have made the best start to a season in the club's 126-year history.
They will go top of the table and put pressure on City on Saturday if they win at Bournemouth (12:30 GMT), with the leaders facing a difficult game at Chelsea at 17:30.
Reds dig deep to keep pressure on Man City
For the first time since May 2017, Klopp started a league match without star forwards Firmino, Mohamed Salah or Sadio Mane.
This was Liverpool's 21st competitive game of the campaign and, with a lunchtime kick-off at Bournemouth on Saturday followed by a must-win Champions League game against Napoli on Tuesday, the Liverpool boss made wholesale changes.
For long periods it looked like the German's decision could backfire.
The much-changed Reds were subdued in a first half in which they lost defender Joe Gomez - one of the four survivors from Sunday's line-up - to an ankle injury following a challenge with Mee.
Nevertheless Clarets keeper Joe Hart still had to save well from Daniel Sturridge and Naby Keita when the game was goalless and the visitors' evening got worse when they conceded in the top flight for the first time since 3 November.
But soon after Milner cancelled out Cork's goal, leading scorer Salah and Firmino were introduced and Liverpool finally took control.
Firmino was in the right place to slide in only his second top-flight goal in three months after a terrific assist from Van Dijk while Phil Bardsley cleared another effort by Keita off the line in the closing stages.
In a frantic finish, Alisson stretched to keep out Mee's header before Shaqiri finished emphatically after an excellent breakaway involving Sturridge and Salah.
Burnley played with energy and purpose for long spells yet remain one point from safety in 19th spot after a 10th top-flight defeat.
This was a much-improved performance compared to the 2-0 defeat to Crystal Palace in their previous game.
With the game goalless, Chris Wood had a shot deflected just wide while Bardsley went even closer to his first goal for the club with a sweet strike.
Ashley Barnes had a goal ruled out for offside before Cork had the home fans dreaming of a first Premier League win since 30 September after Liverpool failed to clear a corner.
But Liverpool's quality substitutes proved the difference as Burnley conceded their 31st and 32nd top-flight goals of the season.
Having taken two points from the last 24 on offer, Burnley need to start turning hard-working performances into points quickly - or face a tough winter in the bottom three.
Naby Keita made a flying start to his Liverpool career in August but injuries have prevented him making a significant impact in the last two months. However the Guinea midfielder was effective at both ends of the pitch against Burnley, deflecting Chris Woods' shot wide at one end before forcing Joe Hart to tip a blistering shot on to a post
Liverpool manager Jurgen Klopp: "Burnley had this specific plan, they wanted to be really aggressive.
"I was really happy we could go into half-time and adjust a few things. We made life difficult for ourselves.
"We controlled the game in a lot of moments. The second half was the perfect reaction and I'm really happy about the three points."
Burnley manager Sean Dyche: "The minimum we wanted was a performance and that was much more like us.
"The important thing now is we have to keep delivering that level of performance because if we do we are still a force in the Premier League.
"The crowd were absolutely fantastic and they are right with us. It all starts with tonight's performance now and that has to be close to the benchmark and we have to build on that."
Burnley are back at Turf Moor on Saturday for the visit of Brighton (15:00 GMT), while Liverpool are in action earlier in the day away at Bournemouth (12:30)