An incredible strike from Jordan Henderson ensured Liverpool got their Champions League campaign off to a winning start, with the Reds beating Milan 3-2 in a thoroughly entertaining clash.
Energised by a raucous home crowd, the Reds got off to flying start, barely allowing their opponents out of their half.
It did not take them long to poke their noses in front, with Alexander-Arnold latching onto Mohamed Salah's clever pass before firing an effort past Mike Maignan - via a sizable deflection off of Fikayo Tomori.
It was nearly 2-0 soon after, only for Salah to see his penalty well saved by Maignan after a handball in the box. Liverpool continued to dominate, registering more than ten attempts before they were shocked by a Milan counter-attack which Ante Rebic finished coolly to level up the scores.
Incredibly, the Rossoneri then took a shock lead after putting together another terrific move in transition that was eventually slid home by Brahim Diaz.
Liverpool came out strong after the break and nabbed an equaliser when Divock Origi found Salah's run with a clever, scooped pass and the Egyptian poked the ball into the net. The Reds continued to turn the screw and eventually got their reward when Henderson netted a wonder goal with 20 minutes left to play.
The closing stages were fairly comfortable for Liverpool and they held on to earn all three points in a classic Champions League group game.
1. Goalkeeper & defenders
Alisson (GK) - 5/10 - Questions might be asked of him for both first-half goals. He probably should have done better.
Trent Alexander-Arnold (RB) - 7/10 - He was electric in the opening exchanges, causing Milan all manner of problems. Continued to impress throughout, although his influence waned somewhat in the second half.
Joel Matip (CB) - 5/10 - A real threat from set pieces and he perhaps should have scored from one in the first half. Poor for both goals, it has to be said.
Joe Gomez (CB) - 6/10 - Encouraging to see him back after a long layoff. Caught out slightly for Milan's second but he was largely pretty solid.
Andrew Robertson (LB) - 7/10 - Motored up and down the left wing all night. Won the penalty and created a host of chances for his team, finishing the game with three key passes.
Fabinho (CM) - 7/10 - Key to Liverpool's dominance in the middle of the park. He broke up play with startling regularity, completing four tackles and six interceptions.
Naby Keita (CM) - 5/10 - Underwhelming. His decision making was sorely lacking in the final third.
Jordan Henderson (CM) - 8/10 - A pass master and did plenty of defensive work too, before scoring an iconic, winning goal. What. A. Hit.
Mohamed Salah (RW) - 7/10 - Always the one making things happen. Made up for his penalty miss with a fine goal early in the second half.
Divock Origi (ST) - 7/10 - Played his part in Liverpool's devastating press early on. Showed great invention to get the ball to Salah for the Reds' second goal. Perhaps he does have an Anfield future after all?
Diogo Jota (LW) - 7/10 - Threatening, taking up some dangerous positions and interchanging with Origi. Denied a goal in the second half by a fine Simon Kjaer block.
Sadio Mane - 6/10 - Not involved all that much, which was surprising.
Thiago Alcantara - 6/10 - Helped Liverpool see things out by being tidy in possession.
Curtis Jones - 6/10 - Looked good after coming on. More than good enough to provide support from the bench this season - and maybe more.
James MIlner - N/A
Alex Oxlade-Chamberlain - N/A
5. Goalkeeper & defenders
Mike Maignan (GK) - 6/10 - Made some terrific stops - including a penalty save - in the first half. However, he misjudged things fatally for Salah's goal.
David Calabria (RB) - 6/10 - Tested by Jota's clever positioning and his night got even tougher when Mane came on. Largely, he coped okay.
Simon Kjaer (CB) - 6/10 - A few sloppy moments but he also came up with some vital blocks.
Fikayo Tomori (CB) - 7/10 - Unfortunate to deflect Alexander-Arnold's cross into his own net early on. After that he made a string of important interventions.
Theo Hernandez (LB) - 6/10 - Had spurts of looking seriously dangerous on the attack. Defensively though, he struggled to contain the pairing of Salah and Alexander-Arnold.
Ismael Bennacer (CM) - 5/10 - A bit overwhelmed by Liverpool at times. The game rather passed him by.
Franck Kessie (CM) - 7/10 - An archetypal box-to-box midfield performance. He contributed in the final third and snuffed out danger in the half-spaces all evening.
Brahim Diaz (AM) - 7/10 - Drifted in and out of the game but reacted swiftly to score his side's second goal.
Alexis Saelemaekers (RW) - 6/10 - Seemed extremely fired up but did not influence things too much before being taken off on the hour mark.
Ante Rebic (ST) - 8/10 - So good on the counter. He took the opener so well and was involved in the second too. Zlatan Ibrahimovic's injury proved to be a blessing in disguise.
Rafael Leao (LW) - 6/10 - Lost Alexander-Arnold for the opener. A bit of a passenger for the most part but he was clinical when it mattered, creating Milan's equaliser with a clever pass.
Olivier Giroud - 5/10 - A strange sub. He offered little.
Alessandro Florenzi - 5/10 - Industrious but had little impact.
Sandro Tonali - 7/10 - Added some much-needed steel. Should have started.
Daniel Maldini - N/A