Holders Manchester City were knocked out of the League Cup as a youthful Newcastle side earned the club's first win in 12 attempts at Etihad Stadium.
Teenage forward Rolando Aarons put the visitors ahead with an angled drive into the far corner.
Newcastle keeper Rob Elliot superbly denied Stevan Jovetic before his skipper Fabricio Coloccini sliced against the post before half-time.
Moussa Sissoko slid in the second as Newcastle reached the last eight.
Now they will travel to Premier League rivals Tottenham in the next round, bidding for a place in the semi-finals for the first time since 1975-76.
Newcastle's players embraced in a celebratory huddle at the final whistle after reaching the quarter-finals of a domestic cup competition for the first time under boss Alan Pardew.
Magpies supporters had called for Pardew to be sacked after a poor start to the campaign in which their team failed to win any of their first six Premier League matches.