Inzaghi scored a freak opener in first-half injury time, unwittingly deflecting Andrea Pirlo's free-kick past a wrong-footed Pepe Reina.
Steven Gerrard missed a glorious chance to equalise before Inzaghi slid home a second eight minutes from time.
Dirk Kuyt pulled one back with a header with a minute left, but time ran out.
Liverpool, as expected, used Kuyt as a lone front man with captain Gerrard pushed into an advanced role.
And it was a ploy that worked well until Liverpool conceded unfortunately in the dying seconds of the first half.
Jermaine Pennant was also prominent as Liverpool posed the greater threat, forcing a fine save from Dida after Marek Jankulovski had conceded possession.
The much-touted Brazil star Kaka was a peripheral figure early on, but he brought a comfortable save from Liverpool keeper Reina with a 20-yard drive.
Alonso then came within inches of putting Liverpool ahead after 26 minutes, sending an angled drive just wide after more poor Milan defending.
But after controlling the game, Liverpool conceded needlessly in first-half injury time.
Alonso had committed several careless fouls, and he paid the price for another infringement on Kaka 20 yards out.
Pirlo's free-kick took a crucial deflection off Inzaghi that completely wrong-footed Reina.
Liverpool struggled to exert their superiority in the early stages of the second half and Benitez made a change after 58 minutes, sending on Harry Kewell for Bolo Zenden.
Gerrard had Liverpool's best chance on 62 minutes when he was sent clear by a dreadful pass by Rino Gattuso, but his finish was weak and Dida saved.
Time was running out for Liverpool and Benitez made a second change with 13 minutes left, sending on Peter Crouch for Javier Mascherano.
As Liverpool pushed forward, they were punished by a piece of brilliance by Kaka and a trademark ruthless finish from Inzaghi.
Kaka unlocked Liverpool with a glorious pass and Inzaghi rounded Reina before scoring from an angle.
Crouch then tested Dida with a 25-yard drive as Liverpool tried to mount an unlikely recovery.
Liverpool pulled one back in the dying seconds when Daniel Agger flicked on Pennant's corner and Kuyt headed home.
But this time there was no dramatic comeback and Milan celebrated wildly.
Steven Gerrard missed a glorious chance to equalise before Inzaghi slid home a second eight minutes from time.
Dirk Kuyt pulled one back with a header with a minute left, but time ran out.
Liverpool, as expected, used Kuyt as a lone front man with captain Gerrard pushed into an advanced role.
And it was a ploy that worked well until Liverpool conceded unfortunately in the dying seconds of the first half.
Jermaine Pennant was also prominent as Liverpool posed the greater threat, forcing a fine save from Dida after Marek Jankulovski had conceded possession.
The much-touted Brazil star Kaka was a peripheral figure early on, but he brought a comfortable save from Liverpool keeper Reina with a 20-yard drive.
Alonso then came within inches of putting Liverpool ahead after 26 minutes, sending an angled drive just wide after more poor Milan defending.
But after controlling the game, Liverpool conceded needlessly in first-half injury time.
Alonso had committed several careless fouls, and he paid the price for another infringement on Kaka 20 yards out.
Pirlo's free-kick took a crucial deflection off Inzaghi that completely wrong-footed Reina.
Liverpool struggled to exert their superiority in the early stages of the second half and Benitez made a change after 58 minutes, sending on Harry Kewell for Bolo Zenden.
Gerrard had Liverpool's best chance on 62 minutes when he was sent clear by a dreadful pass by Rino Gattuso, but his finish was weak and Dida saved.
Time was running out for Liverpool and Benitez made a second change with 13 minutes left, sending on Peter Crouch for Javier Mascherano.
As Liverpool pushed forward, they were punished by a piece of brilliance by Kaka and a trademark ruthless finish from Inzaghi.
Kaka unlocked Liverpool with a glorious pass and Inzaghi rounded Reina before scoring from an angle.
Crouch then tested Dida with a 25-yard drive as Liverpool tried to mount an unlikely recovery.
Liverpool pulled one back in the dying seconds when Daniel Agger flicked on Pennant's corner and Kuyt headed home.
But this time there was no dramatic comeback and Milan celebrated wildly.
AC Milan: Dida, Oddo, Nesta, Maldini, Jankulovski (Kaladze 79), Gattuso, Pirlo, Ambrosini, Seedorf (Favalli 90), Kaka, Inzaghi (Gilardino 88).
Goals: Inzaghi 45, 82.
Goals: Inzaghi 45, 82.
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