Newcastle's 18-year-old winger Rolando Aarons struck in the sixth minute to hand the visitors an unlikely lead before Moussa Sissoko ended any hopes of a City fightback with a brilliant goal to gift underfire manager Alan Pardew a third win in 11 days.
               
"We are buzzing in the dressing room. It has given the club a massive lift. It's been a great week," Aarons said.
               
The result completed a miserable week for City, who are now without a win in three games, after they lost to West Ham United on Saturday and threw away a two-goal lead to draw with CSKA Moscow in the Champions League last Tuesday.
               
Elsewhere, Graziano Pelle scored twice as in-form Southampton let slip a 2-0 lead before advancing to the last eight with a thrilling 3-2 victory against Stoke City.
               
Tottenham Hotspur eased through to the quarter-finals with a routine 2-0 win against Championship (second tier) Brighton & Hove Albion.
               
Newcastle, buoyed by successive Premier League wins started with plenty of intent and their harassing and tenacity in midfield gifted them an early goal.
               
City's Fernandinho was caught in possession and the ball was seized upon by Aarons who surged into the box and finished superbly through the legs of goalkeeper Willy Caballero.
               
That set-back sparked the hosts into life, but the closest they came in the opening period was when Newcastle's Fabricio Coloccini miscued a relatively routine cross onto his own post.
               
For all City's pressure, they could have found themselves 2-0 down at halftime but Martin Demichelis's timely challenge denied Adam Armstrong.
               
City continued to press after the break but could have conceded a penalty when Aleksandar Kolarov felled Gabriel Obertan, who earlier had a goal ruled out for offside, as the Frenchman burst into the box.
               
In the 75th minute Sissoko powered his way through City's static defence and clipped a brilliant finish past Caballero with the outside of his right foot to give the visitors an unassailable lead.
           
Southampton's top scorer Pelle has been a revelation since his close-season move from Dutch side Feyenoord and the imposing Italian forward gave the visitors the lead with a superb goal.
               
The 29-year-old was afforded too much space by the Stoke defence and was able to curl in a sublime strike.
               
On the half hour Southampton doubled their lead with Shane Long sweeping home his first goal for the club at the end of another flowing attack.
               
Stoke pulled a goal back through Steven N'Zonzi's low strike early in the second half and restored parity through Mame Biram Diouf in the 82nd minute.
               
As extra time beckoned Pelle bundled home his ninth Southampton goal of the season in the 88th minute just moments after Stoke had been reduced to 10 men after Peter Crouch's red card.
               
At White Hart Lane, Tottenham dominated possession but failed to take the lead until the 54th minute when Erik Lamela danced into the area before dispatching a neat finish.
               
Harry Kane converted Roberto Soldado's parried shot for a deserved second.

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