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Their 22nd successive top-flight win at home, breaking the English record set by Bill Shankly's side in 1972, was sealed by goals from Mohamed Salah and Sadio Mane after Callum Wilson had given Bournemouth a shock lead.
It restored Liverpool's 25-point lead over Manchester City at the top of the table and three more wins are all that are now required to rubber-stamp their first title for 30 years.
Tottenham Hotspur avoided a third straight defeat in the league with a Dele Alli penalty earning them a 1-1 draw at Burnley, after New Zealand forward Chris Wood had given the Clarets an early lead.
The result did little to help Jose Mourinho's side's bid for Champions League qualification however, leaving Spurs in eighth place, four points behind fourth-placed Chelsea.
Goals were in short supply elsewhere, especially at Molineux where Wolverhampton Wanderers spurned a golden chance to move above Chelsea and into the top four as they were held 0-0 at home by relegation scrappers Brighton & Hove Albion.
Brighton's point was all the more precious as the other sides in the relegation mire lost.
They have 29 points in 15th place, two points ahead of a trio of sides immediately below them.
Alexandre Lacazette's late goal gave Arsenal a 1-0 win over West Ham United, putting them on 40 points in ninth place.
West Ham are 16th, above Watford and Bournemouth on goal difference.
Watford came back to earth with a bump following their 3-0 win over Liverpool last weekend -- Jordan Ayew scoring the only goal in a 1-0 win for Crystal Palace.
Bottom club Norwich City's hopes of survival took another hit as they lost 1-0 at Sheffield United who moved up to sixth place, level on 43 points with Wolves. Norwich are still only six points from the safety zone but time is running out.
Newcastle United's relegation fears look all but over, though, after a 1-0 win secured at Southampton by Allan Saint-Maximin's late goal. Southampton played a large chunk of the match with 10 men after Moussa Djenepo was sent off after a VAR review for a stamp on Isaac Hayden.
Liverpool were far from their best but midfielder James Milner said it was important to respond after three defeats in their last four games in all competitions, especially as they face Atletico Madrid next week seeking to overturn a 1-0 deficit in the Champions League last 16.
"It was important that the boys showed great attitude to come back after some iffy results," Milner said.
"It's impossible to go through a season without an iffy spell, but it's about how you are going to come through that and the boys are working hard."
They made the worst possible start when, after nine minutes, Wilson slotted home for Bournemouth although he appeared to get away with a shove on Joe Gomez in the build-up.
Juergen Klopp was furious but celebrated like a man possessed when his side were gifted a 25th-minute equaliser as Jack Simpson lost possession just outside his penalty area and Mane played in Salah to finish lethally for his 70th goal in his 100th Premier League start.
Mane then fired Liverpool ahead after racing on to Virgil van Dijk's through ball. Mane also hit the woodwork in the second half and although the hosts laboured at times they stretched their unbeaten league run at Anfield to 55.