The champions were joined in the last 16 by holders Middlesbrough, Chelsea, Tottenham Hotspur, Newcastle United, Crystal Palace, Everton, Fulham and Southampton. Arsenal, showing 11 changes from the team that started their traumatic 2-0 league defeat at Manchester United on Sunday, had to wait until the 78th minute for the opening goal against City.
Dutchman Robin van Persie claimed it with a neat low finish to a flowing move, his first goal for the club.
Youngster Daniel Karbassiyoon doubled Arsenal's lead before former England striker Robbie Fowler grabbed a stoppage-time consolation for the hosts with his 200th career goal.
A strong Chelsea side edged to a 1-0 win over London rivals West Ham United, Serbian striker Mateja Kezman netting his first goal for the club in the 57th minute.
Chelsea's England midfielder Frank Lampard had a penalty saved but Jose Mourinho's team held on to reach the last 16.
Tottenham came from behind to beat Bolton Wanderers 4-3 after extra time in a thrilling match at the Reebok Stadium, avenging their 2-1 defeat by Sam Allardyce's team in the Premier League on Saturday.
OWN GOAL
Spurs fell behind to a Ledley King own goal but England striker Jermain Defoe levelled before halftime.
Jay-Jay Okocha restored Bolton's lead from the penalty spot, only for Tottenham defender Goran Bunjevcevic to score from close range on 84 minutes and send the game into extra time.
Substitute Michael Brown headed Spurs in front and Defoe opened up a two-goal advantage with his second before veteran Bolton striker Les Ferdinand gave last season's runners-up hope with a firm header but they could not find an equaliser.
Newcastle beat Norwich City 2-1 thanks to goals by England midfielder Jermaine Jenas and a Shola Ameobi penalty, and Lee Carsley and Marcus Bent were on target in Everton's 2-0 win over Preston North End.
Third division Colchester United took a surprise 1-0 lead at Southampton, who were rescued by a second-half hat-trick from substitute Dexter Blackstock that inspired the Premier League side to a 3-2 victory.
Szilard Nemeth and James Morrison earned Middlesbrough a two-goal cushion at halftime against Coventry City and Danny Graham sealed a comfortable 3-0 victory. Crystal Palace battled to a 2-1 win at Charlton Athletic in a bruising south London derby, Sandor Torghelle claiming the winner before being sent off, while Fulham's Mark Pembridge scored the only goal of the game to sink Birmingham City.
Manchester United, Liverpool, Portsmouth, Nottingham Forest, Cardiff City, Watford and Burnley reached the fourth round on Tuesday.
