Goals from Kevin De Bruyne and Raheem Sterling will see City take on Arsenal in the last four of the competition next month.
It could have been different if substitute Dwight Gayle had equalised when he missed a glorious chance just before Sterling's wonder goal in the second-half.
Apart from that scare, City dominated the contest as they look to win back-to-back FA Cups.
Birthday boy De Bruyne scored his third successive penalty to break the deadlock in the 37th minute.
City had been all over Newcastle at that point, but gave them a golden chance, which they took, when Federico Fernandez pushed Gabriel Jesus over in the box.
Riyad Mahrez went close on two occasions in the opening 45 minutes as the Magpies were fortunate to only be a goal down at the break.
Newcastle boss Steve Bruce reverted to a back-four for the second-half with his five-man defensive set-up struggling to get his side up the pitch.
And his tactical change, along with the introduction of Dwight Gayle for Andy Carroll, almost paid dividends in the 66th minute.
Nicolas Otamendi cheaply gave the ball away near City's box as Allan Saint-Maximin crossed to Gayle, who somehow blasted over from close range.
And the Magpies were made to pay for that miss as Pep Guardiola's men doubled their advantage two minutes later.
Phil Foden excellently controlled Aymeric Laporte's cross-field pass and played the ball to Sterling, who curled it past Karl Darlow from 20 yards.
City will play Arsenal in an FA Cup semi-final clash at Wembley next month.
Man City advanced to the FA Cup semi-finals with a 2-0 win at Newcastle on Sunday.