It truly was an opening night for the ages on Merseyside, playing host to European royalty as Liverpool welcomed the Rossoneri to Anfield for the first time.
The Reds' vibrant start was rewarded when Fikayo Tomori deflected in Trent Alexander-Arnold's cross after a marauding run from the young right-back.
Mo Salah went on to miss a penalty soon after and the visitors punished the costly error before the interval, with goals from Ante Rebic and Brahim Diaz within the space of two minutes.
Salah exacted revenge with a well-worked goal to bring the sides back level before Jordan Henderson's lethal shot beat Mike Maignan from outside the box 20 minutes from time.
The win extends Milan's miserable record of just one win in 14 against English opposition upon their return to Europe's premier competition after eight years, and puts Jurgen Klopp's men top of Group B following Ateltico Madrid's 0-0 stalemate with Porto.
Story of the match
“We need to be intelligent on the pitch and understand where the space is- Liverpool want to push and won’t want to sit back and wait,” was the cry from Milan boss Stefano Pioli before kick-off.
Liverpool's intent was evident from the outset, suffocating rare spells of Milan possession to progress up the pitch in an effort to break the deadlock.
The Reds' first chance spawned from Diogo Jota's penetrative run through the midfield to find a rapid Andy Robertson on the left flank, with the Scotland captain whipping in a thunderous cross for Divock Origi who miscued his effort wide.
Robertson turned provider for Jota in the next phase of relentless pressure, cutting the ball back with the Portuguese feigning his way through the defence for his shot to be intercepted by Fikayo Tomori.
The goal that seemed inevitable arrived via Trent Alexander-Arnold, encapsulating the industry shown by his side in the opening ten minutes with a give-and-go with Salah to cut infield and have his cross deflected in via the former Chelsea man.
Tomori himself prevented Salah capitalising on momentum with a last-ditch recovery following a venomous strike from the Egyptian after some typical deft footwork.
Such was the velocity of the game that much of the raucous home faithful were caught up in the frantic occasion and were unaware that referee Szymon Marciniak had indeed awarded Klopp's side with a penalty, after Ismaël Bennacer's raised arm sent Robertson's volleyed effort wayward.
The recently annointed Premier League '100 Club' man, who had converted his last 17 penalties, had his hot streak from the spot ended by Milan's new signing between the sticks Mike Maignan, who also palmed away Jota's headed follow up.
Liverpool's unprecedented 13 attempts in the opening 15 minutes, 6 of them on target, required somewhat of a necessary drop-off in intensity from the Reds, with Milan's first registered shot from Theo Hernandez arriving 30 minutes in.
Milan's threat up until the final five minutes of the half was blunt and frequently snuffed out by an on-form back line featuring Joe Gomez for the first time since November 2020.
Ante Rebic, whose place in the starting 11 was brought into question with the return of Olivier Giroud from coronavirus, put away his first goal of the season after a fantastic flowing move from the visitors.
A combination of a stand-off Liverpool midfield and a defence lost at sea enabled some slick interplay between Alexis Saelemaekers, Rafael Leão and the Croatian who slotted home.
Former Manchester City winger Brahim Diaz dealt the sucker-punch blow to send a bemused Liverpool a goal behind at the break, sliding in to undo Robertson's goal-line block and, perhaps in the grander scheme of things, Liverpool's dominance following a clinical counter-attack.
The narrative of a second half comeback against Milan in European competition almost writes itself, and Mo Salah was the man to etch his name into the story of the match and avenge his penalty miss three minutes into the second period.
Salah was able to get on the end of a lofted Origi ball and take advantage of a hesitant Maignan to poke home, with celebrations muted from the winger for fear of his potential offside positioning that was consequentially unfounded.
Hello, here we go.
Just as in the first half, Liverpool's swagger and confidence following a goal, in this case Salah's equaliser, saw them maintain the lion's share of possession.
Sadio Mane and Olivier Giroud were introduced not long after the hour mark- two men who secured their sides' respective results against Leeds United and Lazio at the weekend and were desperate to do the same at Anfield.
While the Senegalese's first effort left a lot to be desired, the same could not be said for a certain captain fantastic rising to the occasion when it matters.
Following a vital block from Simon Kjaer to deny Jota, the resulting corner was headed away by Bennacer and found it's way to Jordan Henderson, who, on the half-volley, rifled in Liverpool's third and most crucial of the night.
A coming together with Franck Kessié and Liverpool's Brazilian contingent of Thiago Alcantara and Fabinho in the box evoked an almost audible, sharp intake of breath in Anfield with the crowd unable to decipher Szymon Marciniak's call, with the Polish official crucially awarding a free-kick in favour of the home side in what was tentative closing stages for the Reds.
A teasing flick on from a corner from Kjaer went begging in front of Diaz and Daniel Maldini, finding it's way into the arms of Alisson Becker.
James Milner's cameo late on was everything Klopp and Liverpool fans would want and more late on, with tactical fouls and retaining the ball consistently to help secure a famous win on one of those European nights at Anfield.
Jurgen Klopp's declaration in his pre-match press conference that a fixture of this calibre will be a "must watch" was a foreboding one to say the least.