Brendan Rodgers' men took an early 2-0 lead but let it slip almost immediately and were plagued by errors throughout. The firepower of Daniel Sturridge and Co. saw them scrape the three points, though, in what was a highly entertaining game.
Let's take a tactical look at how this one played out.
Liverpool lined up in a certifiable 4-3-3, with Steven Gerrard the deepest in midfield, Daniel Sturridge on the right and Raheem Sterling on the left.
Swansea City adopted a 4-2-3-1 led by Wilfried Bony, with Neil Taylor in for Ben Davies at left-back and former Red Jonjo Shelvey in the No. 10 role.
The game had barely got going before Sturridge reliably broke the deadlock, scoring in his eighth consecutive game for Liverpool.
Both sides traded short spells of possession before Sterling robbed Angel Rangel of the ball and sliced the Swansea defence apart with a scything, outside-of-the-boot through-ball that set his striker one vs. one with Michel Vorm.
It's yet another example in a growing list of how the Reds look far more dangerous on the counter-attack than they do in patient buildup play, and what was thought to be a possession-based machine is quickly making a name for itself as a counter-king.
During the transition, the flexibility of Liverpool's front three came to the fore: Sturridge was playing centre-forward, Luis Suarez left wing and Sterling tracking back in his own third.
The goal didn't faze Swansea, and they continued with their original game plan of working the ball into Bony's feet as much as possible so he could lead the forward play.
The Ivorian has had his good days and his bad days in the Premier League, but he was in irresistible form early on. Initially, Liverpool committed one man to mark him, but that quickly became two and even developed to three.
Dropping deep to receive the ball, he was a true threat, and he brought both of his wingers heavily into the game.
When the midfield began keying on him, it created space for others to exploit; Jonjo Shelvey began roaming into vast swathes of territory untouched as Steven Gerrard and Jordan Henderson were dropping to help with Bony, and plenty of other players found room to operate.
"Give It Away Now"
Liverpool raced to a 2-0 lead after just 20 minutes, but the Reds continually made life difficult for themselves.
Bony won an unchallenged aerial in the buildup to Jonjo Shelvey's retort, with wingers Wayne Routledge and Nathan Dyer roaming untracked, too.
Martin Skrtel was the chief culprit among many in Liverpool's midfield and defence who gave the ball away in dangerous areas often, while Martin Skrtel over-ran a dribble and fouled Shelvey to give away the equalising header.
Having been the benefactors of similarly ludicrous play during their 5-1 win over Arsenal just a few weeks ago, it was incredible to see the Reds committing a host of errors themselves.
You cannot surrender possession in your own third while moving through passing transitions this easily. In the Premier League, you will pay.
Swansea had far more success working the ball forward in central areas and out of midfield in the first half, and that was largely down to Bony's brilliance as an orthodox target man.
Liverpool were the complete opposite, as their first two goals came from individual brilliance/searing counters and the midfield struggled to move the ball through the zones.
Coutinho's energetic pressing disrupted Jack Wilshere badly when the Reds met Arsenal a few weeks ago, and the Brazilian performed a similar role here. His harrying of Jonathan de Guzman in particular threw the Dutch-Canadian off his game.
It took Rodgers' side 35 minutes to craft their first successful attack borne from a central area, and it inevitably ended with a goal. Sturridge headed home a Suarez cross from the left, but it all started from Henderson's surge forward from deep.
The Englishman sprinted forward to force Swansea's defensive line to drop deep and pick him up, which created a temporary pocket of space between defence and midfield. It was the first time it had opened up, and the Reds' incredible attack took full advantage.
Joe Allen Adjustment
In the first 10 minutes of the second half, Skrtel hauled Bony down for a penalty and gave the ball way twice in dangerous areas.
Rodgers sought to rectify the damage by making a substitution, but he confused Anfield by subbing off Sterling for Joe Allen—a right-winger for a deep-lying central midfielder.
But it was the right move, and it paid dividends in the end: It allowed Coutinho (another culprit for misplaced passes) to move to the left wing and Allen to slot in alongside Henderson and Gerrard.
This removed two of the turnover threats for the Reds, as Skrtel would simply pass it to Allen and Coutinho was not there to give it away deep in transitions. The Brazilian's passing can be magnificent, but he takes risks he simply mustn't when playing in a flat three.
Allen managed 95 percent pass accuracy, per WhoScored?, and steadied the ship with good pressing and confident, clean passing. It also freed up Henderson for a more expansive role, and his gamble surging into space (again) paid off as he stabbed home the fourth and final goal.
There were more odd ends that will have both impressed and disappointed Rodgers in summarising his team's performance, with Jon Flanagan's improved handling of Routledge contrasted with Victor Moses' ineffectual 15 minutes chief among them.
Allen proved his worth to this midfield once again, Henderson took another step closer to the World Cup and Sturridge could have had a hat-trick.
Swansea played well, moved the ball with pace and allowed Bony to dominate the centre-back pairing and feed off it. Garry Monk will be perplexed as to how his side scored three at Anfield and still lost.
The story of the day, though, will be the Reds' extremely questionable defence and poor play in transitions. A team looking to sustain a top-four challenge simply cannot ask their attack to bail them out every week without fail.
For the neutrals, however, this was fantastic.
Tactical Man of the Match: Jordan Henderson