A drenched Jurgen Klopp was in serious danger of enduring another bout of the January blues.
Johann Gudmundsson's late equaliser appeared to have wrestled two points from Liverpool's grasp. It would have been one of those draws which felt like a crushing defeat.
But deep into stoppage time up stepped a couple of unlikely heroes to kick-start the new year with memorable scenes of unbridled joy in front of the travelling Kop. There was no hangover here.
Dejan Lovren headed Alex Oxlade-Chamberlain's free-kick goalwards and Ragnar Klavan stooped to force it home from close range.
It was the veteran Estonian defender's first Premier League goal and only his second for the Reds in 44 appearances.
The sense of irony won't have been lost on Klopp. On the day that Liverpool unveiled £75million signing Virgil van Dijk , the two centre-backs arguably most at risk of dropping down the pecking order following the Dutchman's arrival delivered a dramatic late twist in the tale at Turf Moor.
No wonder Klopp, who has worked so hard to instil that kind of never-say-die spirit, unleashed a flurry of fist pumps after the final whistle.
A gruelling festive schedule of four games in the space of 10 days has yielded 10 points out of a possible 12. But for that five-minute meltdown at the Emirates it would have been perfect.
Liverpool's hopes of retaining their top-four status have been significantly strengthened. Catching Manchester City might be a pipe dream but second spot is a realistic target between now and May.
This triumph was arguably the sweetest of the lot as Liverpool had to dig so deep amid monsoon conditions to achieve it.
No Mohamed Salah, no Philippe Coutinho, no problem. That gifted duo were absent with 23-goal top scorer Salah nursing a groin problem and Coutinho hampered by a thigh problem.
With Roberto Firmino given a breather, Liverpool were without three of the front four who have inflicted so much damage so far this term. The other member, Sadio Mane, enjoyed a much needed injection of belief as his stunning strike broke the deadlock.
In the main this was a day for those on the fringes to step up and deliver and they didn't disappoint. Liverpool weren't particularly fluent or pleasing on the eye, but in terms of organisation, attitude, desire and discipline this was a truly gutsy team effort.
A year ago Liverpool's season went off the rails following the turn of the year as a lack of depth was exposed. In fact prior to this contest, Klopp had won just four out of 18 matches in the month of January during his Anfield reign.
But this time around they look so much better equipped to cope with the demands facing them. Klopp made seven changes but was also able to call upon proven class.
There was the welcome sight of Adam Lallana making his first start of the campaign after finally overcoming the thigh injury he suffered in pre-season. The England international will need time to get up to speed but his creative spark and work ethic will be a massive bonus over the weeks and months to come.
Alex Oxlade-Chamberlain, who departed to a warm ovation from the away end late on, was the pick of the bunch as he continues to look every inch a Liverpool player. Playing on the left of the front three, the £35million man was positive and direct throughout.
Lovren, Joe Gomez, Emre Can and Mane were the only players retained by Klopp following Saturday's hard-fought 2-1 win over Leicester City.
Dominic Solanke was tasked with leading the line and the young striker, who is still learning his trade, could hold his head high. He had precious little service during a scrappy contest but he put himself about and gave everything for the cause.
Liverpool dominated possession in the first half but did precious little with it. Moves repeatedly broke down on a heavy surface as passes went astray.
Clearly wary about a repeat of last season when the Reds were undone on the counter by the Clarets, Klopp had both Can and Gini Wijnaldum sitting deep and providing protection for the back four.
Oxlade-Chamberlain's sweetly struck 25-yarder was kept out by Nick Pope as chances remained at a premium. The combative Solanke chased lost causes and won his share of aerial duels but showed his inexperience by giving away some cheap free-kicks.
As the rain hammered down, it wasn't pretty but Liverpool refused to be bullied as they stood up to the physical challenge in all departments.
Lallana actually made his most important contribution tracking back, sliding in to make a crucial last-ditch tackle on Gudmundsson as he hooked the ball to safety.
Stand-in skipper Simon Mignolet clung on to Scott Arfield's header after Can's misplaced pass had left Liverpool outnumbered.
Lovren and Klavan both shone as they coped admirably with the menace of Ashley Barnes, whose knock down was drilled just wide by Arfield.
When Liverpool attacked a combination of the conditions and the absence of key personnel ensured they lacked their usual potency. Trent Alexander-Arnold picked out Mane, who drifted in field but dragged tamely wide of the post.
The second half brought more of the same as the Reds huffed and puffed. They were crying out for some inspiration and it arrived just past the hour mark.
Alexander-Arnold's first time cross was deflected into the path of Mane on the edge of the box. The Senegal winger controlled with his right foot, turned and hammered an unstoppable left-footer beyond Pope for his eighth goal of the season.
Mane soon made way for Firmino as Klopp sought to kill off the contest. Alexander-Arnold's fierce 25-yarder was clawed away by Pope, who then thwarted Oxlade-Chamberlain to ensure that Burnley stayed in the game.
With Sam Vokes on to partner Barnes, Liverpool had to deal with an aerial bombardment.
Mignolet turned away Vokes' header but was left helpless when the substitute nodded on Charlie Taylor's cross and Gudmundsson arrived at the back post to convert.
A dry January? Lovren and Klavan had other ideas. Liverpool started 2018 the way they finished 2017 - the buzz continues.
Man of the match: Alex Oxlade-Chamberlain. Led the charge throughout.
Source: Liverpool Echo
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