The Reds took the lead early in the first half through a Fikayo Tomori own goal, but Milan went into the half-time break 2-1 ahead thanks to strikes from Ante Rebic and Brahim Diaz.
Liverpool came back with a vengeance in the second half, though, and they were level when Mohamed Salah poked the ball home from close-range in the 49th-minute following a wonderful pass from Divock Origi.
Then in the 69th-minute, the hosts completed the comeback to send their adoring fans inside Anfield wild.
And it was club captain Jordan Henderson who grabbed the goal in stunning fashion, the Englishman's strike from the edge of the box to make it 3-2 evoking memories of a prime Steven Gerrard.
Liverpool 3-2 AC Milan Champions League Highlight Show | Football Terrace
Take a look at his wonder-goal here...
Video: Henderson's stunner
What a strike!
A Liverpool comeback versus Milan? We've heard that story before....
Jurgen Klopp's men were by far the better side on the night and they actually managed 11 shots on the Italian outfit's goal inside the first 15 minutes of proceedings.
Milan were just unable to contain Liverpool's brilliant right-hand side pairing of Trent Alexander-Arnold and Salah throughout the game and it was no surprise to see the Reds eventually secure the three points.
The victory is certainly a big one for the Premier League team, given that they're in the hypothetical 'Group of Death' this season.
Games home and away against both Atletico Madrid and FC Porto await, as well as a trip to San Siro before the end of the year.