Sergio Aguero guaranteed the win with the second goal
Manchester City are in to the last four of the FA Cup for the first time since 2013.
The Sky Blues have beaten fellow Premier League side Middlesbrough 2-0 at the Riverside Stadium thanks to goals from David Silva and Sergio Aguero.
City sit third in the Premier League after a disappointing 0-0 draw against Stoke City in midweek left them 10 points off the summit.
With Pep Guardiola's side already unlikely to close the large gap to leaders Chelsea in the remainder of this league season, the FA Cup and Champions League are the realistic trophy opportunities in the Catalan coach's debut season in charge.
After a thriller in the first leg of the last-16 clash against Monaco three weeks ago and the second leg to come next Wednesday, the Champions League remains very much in the balance even at this early juncture.
With the win at Middlesbrough, City are now set for a semi-final at Wembley and are also within one victory of a place in the final at the same stadium.
Silva gave Man City the lead after Pablo Zabaleta's cross from the right made its way across and the Spain international converted from close range for a 3rd minute lead.
A cross from the left for Leroy Sane was finished off by Aguero with 23 minutes to go to seal the quarter-final win.