Aguero’s 23rd goal of the season in all competitions early in the second half ensured a routine win for the holders, three days after sealing back-to-back Carabao Cup triumphs at Wembley.
The Argentinian registered his 254th goal in all competitions for City in 367 appearances – one more than Wayne Rooney scored for Manchester United in 553 matches.
Pep Guardiola’s side crashed out of the FA Cup at the same stage two years ago when losing 1-0 at Wigan, but there was never a hint of an upset at Hillsborough.
Wednesday have slipped out of the Sky Bet Championship play-off picture after winning only one of their nine previous league matches and City rarely ventured beyond second gear.
But otherwise it was an uneventful opening – and things did not get much better.
Jesus should also have done better with Aguero’s diagonal ball over the top as Wednesday retreated into their own half and in the 32nd minute Nicolas Otamendi headed Riyad Mahrez’s free-kick against the crossbar.
Stones met another ball in from Mahrez at the far post, but his downward header bounced over the bar as the first half ended goalless.
Wednesday, 3-0 down at half-time on the same pitch against Derby on Saturday, will have considered the first part of their damage limitation exercise successful.
At the start of the second period Aguero’s effort was gathered by Joe Wildsmith and the Wednesday goalkeeper then brilliantly tipped Mendy’s thumping drive on to the crossbar.
Wildsmith pulled off another superb save to deny Bernardo Silva, but was culpable soon after when City broke the deadlock in the 53rd minute.
Aguero spun on to Mendy’s pass into the box and Wildsmith was only able to parry the Argentinian’s shot up and over the goal-line instead of pushing it clear of danger.
There was a hint of offside to the goal and it may have been checked had a video assistant referee been in operation.
Wildsmith kept out Mahrez’s shot as City chased a second, while Wednesday had failed to muster an effort on target in the second half before Alex Hunt’s rare ball into City’s box just eluded fellow substitute Steven Fletcher.
Late substitute Raheem Sterling was sent on to finish the job and he was also denied by Wildsmith in time added on.