Lionel Messi took his remarkable tally for the season onto 53 with a deadly double, while David Villa and Jordi Alba were also among the goals as Barca offered a timely reminder to those who have had the audacity to write them off on the back of a recent dip in their impeccably high standards.
Milan set up from the off looking to cling on to their two-goal first leg lead, but the Italian outfit's containing job saw them hold out for just five minutes before a moment of magic from Messi brought the tie screaming back to life.
The mercurial Argentine gathered the ball on the edge of the area, after a period of intricate one-touch football from the hosts, and sent a stinging drive arrowing into the top corner, with Milan goalkeeper Christian Abbiati left rooted to the spot.
Barca continued to prod and probe as the visitors sat off, with Abbiati pushed to full stretch as he first tipped an Andres Iniesta volley onto the crossbar and then touched a curling effort from Xavi around the post.
Stephan El Shaarawy was offering the only glimmer of hope for Milan, but the talented forward scuffed two tame shots at Victor Valdes.
Milan were able to create one golden opportunity, though, on 38 minutes, but teenage striker M'Baye Niang fluffed his lines as he raced clear on the counter and slid a low shot onto the foot of the post.
Within 60 seconds the magnitude of that miss was made painfully clear to the visitors, with Massimo Ambrosini losing the ball to Iniesta in midfield and six perfect touches later the ball was in the back of the net - with Messi cutting onto his left foot and drilling past Abbiati from the edge of the box.
Milan were getting sick of the sight of Messi by the time the second half got under way, and he moved ominously through the gears within seconds of the re-start before firing straight at Abbiati.
Barcelona can hurt you in any number of ways, though, and it was Villa who grabbed their third of the evening on 55 minutes, with Kevin Constant's failed attempt to cut out a pass allowing the Spain international to curl home and celebrate in style.
Barca could not afford to relax in the knowledge that one away goal for Milan would swing the encounter back in the Rossoneri's favour, and they suffered a couple of nervy moments at the back as the Serie A side finally came out of their shell and made one final desperate effort to keep their European dream alive.
However, having worked so hard to get their noses in front, Barcelona were not to be denied and Alba made their progress into Friday's last-eight draw a little more comfortable with a composed finish in stoppage time.
David Villa says Barcelona are feeling buoyant and ready to take on all comers after taking another positive step in their quest for European glory.
"When you go through on a night like this, all of the bad days are forgotten," he said.
"After experiencing what we did tonight, we don't care who we get in the quarter-finals."
AC Milan coach Massimiliano Allegri is looking for his side to take the positives from their showing and kick on in their bid to secure a top-three finish in Serie A.
He said: "I am happy with how my players have performed. We are disappointed but this experience will be useful for the future.
"Now our aim is to get to the Champions League next season. This match must allow us to grow."
|2||1st Half Goals||0|
|7||Shots on Target||2|
|4||Shots off Target||5|
|75||1st Half Poss.||25|
|61.2||2nd Half Poss.||38.8|