Holders Palace suffer biggest ever FA Cup shock, Man City hit 10
In their last FA Cup outing at Wembley in May, Palace made history by beating City to win the club's first ever major trophy.
They entered the record books for the wrong reasons this time at Moss Rose as captain Paul Dawson and Isaac Buckley-Ricketts scored either side of half-time for the side managed by John Rooney, the younger brother of former England captain Wayne Rooney.
The 117 places that separate Premier League outfit Palace from Macclesfield of the National League North in the English football pyramid is the most ever overcome by an underdog in FA Cup history.
"I can't believe it, we never thought we would be in this position," said Rooney.
"I didn't think it was possible but there is that little bit of hope that anything can happen on the day."
Palace boss Oliver Glasner was furious at what he described as a lack of "pride" and "slapstick" defending by the Eagles, who are now winless in nine games.
"I have no explanation for what I have seen today," said the Austrian, who has been linked with the vacant managerial role at Manchester United.
Semenyo scores
Just a day after securing his £65 million ($87 million) move from Bournemouth, Semenyo was among the scorers as City put League One Exeter to the sword at the Etihad.
Erling Haaland started but was remarkably not among the goals before being withdrawn at half-time.
Rico Lewis scored twice, while Max Alleyne, Rodri, Rico Lewis, Tijjani Reijnders, Nico O'Riley and Ryan McAidoo were also on target for City and Exeter netted two own goals.
Sunderland won another of the all Premier League ties on penalties against Everton afrer a 1-1 draw.
Robin Roefs saved all three of the Toffees spot-kicks in the shootout to send the Black Cats into round four.
Premier League strugglers Wolves are now unbeaten in four games after thrashing Shrewsbury 6-1 thanks to a Jorgen Strand Larsen hat-trick.
Fulham needed three goals in the final half hour to beat Middlesbrough 3-1 at Craven Cottage, but Burnley found Championship opposition an easier proposition in thrashing Millwall 5-1.
Brentford cruised to a 2-0 win at financially stricken Sheffield Wednesday.
Tottenham boss Thomas Frank badly needs a win to ease speculation over his future when they host in-form Aston Villa later on Saturday.
Liam Rosenior also takes charge of Chelsea for the first time in the 2000GMT kick-off away at Charlton.