The box was ticked off in memorable style at an electric Nou Camp as Barca kept their bid for a third European crown in five years alive by becoming the first team to overturn a two-goal first-leg deficit without the benefit of an away goal.
The painful memory of their toothless performance in losing 2-0 at the San Siro last month was banished as Lionel Messi struck twice and Barca romped to a majestic 4-0 victory that put them through to the last eight 4-2 on aggregate.
Pressure had mounted in the buildup to Milan's visit after Barca were knocked out of the King's Cup and beaten in La Liga by Real Madrid.
The tension increased further when Real, who Barca may meet in the last eight, eliminated Manchester United to reach the quarter-finals last week.
While their arch rivals prospered, Barca's Champions League dream was hanging by a thread but Xavi, one of the most decorated players ever to play the game, and his team mates responded with a display that will live long in the memory.
"It has been many years since Barca managed an historic comeback and I have not seen the Nou Camp so animated in a long time," Xavi told reporters.
"We pressured them well high up the pitch and we played an exceptional game," added the 33-year-old, who has three Champions League crowns and is also a World Cup and double European championship winner with Spain.
Barca were unrecognisable from the side who limped through the first leg, harrying and hassling Milan from the start and driving forward at any opportunity.
Scoring early was crucial and after Messi struck in the fifth minute and doubled the home side's lead five minutes before the break - moments after Milan forward M'Baye Niang had hit the post - Barca never looked back.
Forward David Villa, who scored Barca's third 10 minutes after half-time, saw little of the ball in his advanced central position but kept centre-backs Philippe Mexes and Cristian Zapata occupied, allowing Messi to exploit the space.
Xavi and Iniesta kept the ball flowing rapidly and their probing runs and passes were a constant threat, while Sergio Busquets was tireless in his unheralded but crucially important defensive midfield role.
Jordi Alba, who netted Barca's fourth to kill Milan off in added time, and fellow full-back Daniel Alves played more like wingers, pushing high up the pitch and repeatedly forcing the Italians into retreat.
Centre-back Gerard Pique had issued another rallying cry before the game, saying Barca had to get past Milan for their ailing coach Tito Vilanova, who has stepped aside and handed the reins to assistant Jordi Roura while he has cancer treatment in New York.
Vilanova is due to complete the programme towards the end of the month and should be back on the bench for the quarter-final, first leg at the beginning of April.
"Tito Vilanova is very happy and he will be able to be present for the next round," Roura told a news conference.
"He watched the game with a huge amount of emotion and he is pleased because we are still
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