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Two minutes into the match Chelsea captain Cesar Azpilicueta gave away a free kick and Tammy Abraham deflected Quincy Promes's whipped cross into his own net.
The Turin side, with 13 points from five games, made sure of winning Group D with one match to spare.
England seeks to lift European soccer's most iconic trophy for the 14th time. Spain has a record 18 titles, though those were won by just two clubs 13 for Real Madrid, five for Barcelona.
The draw had an unusual feel with neither Bayern Munich nor Real Madrid in the hat, the first time both European giants have failed to reach the last eight since 2005-06.
Ajax, who have won the trophy four times, most recently in 1995, reached the last eight of Europe's top competition for the first time since 2003.
Bayern knew they had to be more adventurous than they had been at Anfield, but they were suffocated by Liverpool's intense pressing in the first half.
Ronaldo blasted home the decisive goal from a penalty with four minutes left to seal a 3-2 overall triumph having made the breakthrough in the 27th minute and levelled the aggregate score three minutes after half-time with another towering header.
City's record home win in Europe did not look likely after a quiet opening 35 minutes, but once Sergio Aguero began the rout from the penalty spot it became embarrassingly easy as City reached the last eight for the third time in four years.
Results 281-289
