Huddersfield took the lead through Harry Bunn but Aguero's double - as well as efforts from Leroy Sane, Pablo Zabaleta and Kelechi Iheanacho - ensured that it turned out to be an easy night's work for Pep Guardiola's side.
Middlesbrough lie in wait for City in the quarter-finals, with that fixture scheduled to take place on March 11.
City started on the front foot with Sane striking the post with a volley from an acute angle and Aguero seeing a shot comfortably saved by Joel Coleman, but in the seventh minute they were left stunned as Huddersfield went in front.
Over the course of the next 20 minutes, City had two handball appeals in the area go against them, while Kevin De Bruyne saw a free kick easily saved by Coleman.
However, on the hour mark, they found an equaliser when Raheem Sterling delivered a low cross for Sane to tap home from close range.
Five minutes later, City were awarded a penalty when Jon Gorenc Stankovic was adjudged to have hauled down Nicolas Otamendi, and Aguero was able to convert from 12 yards as he sent the ball into the top corner.
City were now pushing forward in numbers and they soon netted a third when Aguero - who had hit the post a minute earlier - cut the ball back for Zabaleta to find the net from close range.
Despite City's dominance, they almost conceded a second goal towards the end of the first half when Jack Payne was played in behind the City defence, but his effort from 10 yards was too close to Bravo.
Huddersfield needed to carry that threat into the second period and they wasted a glorious opportunity through Joe Lolley, who got in front of his marker before sending a header over the crossbar.
City were still in control of the contest, but they were being restricted to long-range efforts with De Bruyne seeing a free kick tipped wide by Coleman.
However, with 16 minutes remaining, City made sure of their place in the quarter-finals as Aguero produced a smart finish to direct Sterling's cross inside the near post.
Huddersfield forward Collin Quaner should have reduced the deficit in the final minute of normal time but he sliced a half-volley over the crossbar, before Iheanacho capped a bright cameo with a tap-in from inside the six-yard box to wrap up City's progress to the last eight.