Rodrigo Palacio grabbed the first goal of the match when turning home from close range before Marcelo Brozovic scored a beauty to make it two. Ivan Perisic slid home the third to cap off an easy victory.
Despite Inter sitting a division above their opponents, it was the Sardinians who started on the front foot with Davide Di Gennaro hitting a long shot wide of the post.
As the game reached the midway point of the first-half the Nerazzurri began to grow into the match, Palacio on hand to fling himself via a diving header only to be saved at point-blank range.
The Argentinian would not be denied just a few minutes later however, steering home a chance with no one around him from all of six yards following a floated cross into the box.
Just prior to half-time Niccolo Giannetti latched onto a nice through ball from Di Gennaro who then saw his effort well saved by Juan Carrizo.
Five minutes into the second-half saw a wonderful chance fall Cagliari’s way to draw level when a flicked header from Fabio Pisacane spanked the Inter crossbar.
The frantic start continued following Pisacane’s chance, this time with Gary Medel directing a header that left Alessio Cragno flat-footed but also relieved to see it drop wide of his goal.
Brozovic wrapped up the game much to the relief of those in Milan, curling home a possible goal of the knockout stages with a fine strike from all of 25 yards out.
It would not be the end of the goals for the night however, Perisic sliding in a third following the aforementioned Brozovic’s effort hitting the post.
Roberto Mancini’s side will either meet Napoli or Hellas Verona in the quarter-finals.