The Cityzens made ten changes to the side that were held 2-2 by Nottingham Forest in their Premier League clash on Wednesday, with only Matheus Nunes retaining his spot in the starting line-up.
Both teams looked lively from the onset with Tijjani Reijnders narrowly missing the target for the visitors in the opening stanza before the Magpies took the lead through Harvey Barnes in the 17th minute.
City began dominating the match in pursuit of an equalizer and levelled the score Savinho who deflected home a Jeremy Doku low ball in the 39th-minute.
Pep Guardiola's side started the second half with a bang, with Omar Marmoush finishing neatly from a Nunes pullback from the right to overturn the tie.
Toon's manager Eddie Howe made a triple substitution to try and get back into the match, but those hopes were dashed when Marmoush smashed in a long-distance strike to hand City the advantage.
City confined Newcastle to their own half for the rest of the match and were unfortunate to have not scored more goals as they advanced to the next round of the FA Cup.
"We played so good," said Pep Guardiola after the match.
"The first 20 minutes in this stadium that always happens but then Jeremy and Savinho were so decisive. The best performance we have played in this stadium in our time together here.
"It was important to score in the first few minutes of the second half but from the first 20 minutes until the end the game was really good. Everyone was so good, to beat Newcastle here is amazing."