Liverpool required a winning goal from club captain Jordan Henderson, in a pulsating Champions League return to Anfield.
In front of fans in this competition for the first time since March 2020, the reds welcomed the Italian giants to play for the first time in front of The Kop. With 13 European Cup titles this was clearly the standout tie of the evening and both sides had periods in which they excelled.
The reds raced out of the blocks and were utterly dominant in the opening half hour spell in which the reds could easily have scored three or four.
As it was they got off to a great start in the 9th minute when Trent Alexander-Arnold's persistence in front of goal led to a goal with a fortunate deflection - the goal eventually recorded as an own goal by Fikayo Tomori.
Moments later and the reds were awarded a penalty after a handball = but Mo Salah saw his penalty saved by Mike Maignan and Jota's follow up was also stopped by the keeper.
This didn't immediately lead to an Italian renaissance, as the reds continued to mount effective attacks.
Divock Origi was playing in place of Sadio Mane, and at the back Joe Gomez marked his return as he gave Virgil van Dijk an evening off. Both played well at times - a positive sign as the reds begin this fixture heavy period of the season.
Alisson, Alexander-Arnold, Matip, Gomez, Robertson, Fabinho, Henderson, Keïta, Jota, Origi, Salah
Subs: Adrián, Kelleher, Konaté, van Dijk, Mane, Tsimikas, Minamino, Phillips, Oxlade-Chamberlain, Milner, Alcantara, Jones
Despite Liverpool's dominance however they switched off minutes before the ref blew his half time whistle.
In the space of two minutes, two defensive lapses led to Milan goals - with Rebic and Diaz handing the away side an unlikely half time lead.
But the reds rallied in the second half and it was none other than Mo Salah who quickly restored parity just after the break before Henderson unleased a half-volley mid way through the half to eventually claim the points.
Milan pushed hard to get back in the game but the reds managed to hold on to their lead and have a very important opening three points in this 'Group of Death'.
Attention now turns to a visit from Crystal Palace at the weekend, when the reds will hope to continue their strong start to the season and stay amongst the Premier League leaders.