Foden double eases Man City into FA Cup sixth round, Leicester out
Foden struck in the seventh minute but it was not an entirely comfortable night for Pep Guardiola's side until the England forward made it 2-0 in the 74th minute.
Kevin De Bruyne gave the scoreline an emphatic look with a sublime finish from 25 metres although it was harsh on Bristol City who had been on a 12-match unbeaten run.
Leicester were booed off after a 2-1 home defeat by second-tier Blackburn Rovers for whom Tyrhys Dolan and Sammie Szmodics were on target before a Kelechi Iheanacho reply.
Fulham reached the sixth round for the first time in 13 years with superb goals by Joao Palhinha and Manor Solomon earning them a 2-0 win over fellow top-flight side Leeds United.
Brighton and Hove Albion's hopes of a first ever major trophy remained intact as Evan Ferguson's first-half goal sealed a 1-0 win over second-tier Stoke City.