Great stuff from Milan there - you just can't play Barca much better than that.
There were periods where Milan were pinned back on the edge of their own box, but for a fair chunk of the second half they managed to step up and have a pretty good level of control over the game and retain the ball. That allowed some of their players a bit of a rest which meant they were able to keep going through to the end unlike a lot of teams who play Barca (including Milan last season) who were dead at 75 mins.
Key thing was that everything, whether it was sitting deep or stepping up, was done as a unit, so there was never any space left in dangerous areas that Barca could exploit.
That said, I thought Barca were crap. What is the point of having Alba and Alves in your team if you aren't going to have them make penetrating runs from deep to try and get down the side or in behind a packed defence? Barca didn't stretch the game wide or long, so it was comparatively easy for Milan to remain compact. Can't remember a game where Messi was involved so little since Zanetti dominated him a few years back.