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A much-changed Bournemouth were beaten 3-0 by League One Millwall, while Stoke lost 2-0 at home to Championship side Wolverhampton Wanderers.
West Brom lost 2-1 at home to Championship promotion hopefuls Derby.
Everton were beaten by Leicester and Hull knocked out Swansea in two all-Premier League ties.
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Two non-league sides will be in Monday's fourth-round draw after securing replays.
National League leaders Lincoln City came close to causing an FA Cup upset as two goals from former Derby striker Theo Robinson saw them 2-1 up at Ipswich before Tom Lawrence equalised late on.
Lincoln's league rivals Sutton also earned a replay as they draw 0-0 at home to League One AFC Wimbledon.
FA Cup holders Manchester United beat Reading 4-0 in the early game to progress, while 2013-15 and 2014-15 winners Arsenal came from behind to win 2-1 at Preston in the late game.
They were joined in the fourth round by Premier League champions Leicester, who won 2-1 at Everton thanks to an Ahmed Musa double.
New Hull City head coach Marco Silva watched his side beat Swansea 2-0, a result which meant defeat for Swans boss Paul Clement in his first official match in charge.
Watford avoided an upset by overcoming Championship side Burton Albion 2-0.
Brentford came out on top of Saturday's highest-scoring game as the Championship outfit beat non-league Eastleigh 5-1.
A number of games featuring Premier League sides had low attendances as the top-tier clubs entered the competition.
A crowd of 6,608 watched Hull City versus Swansea at the KCOM Stadium, with 210 supporters making the trip from Wales.
At Norwich, who average 26,000 in the Championship, just over 12,000 watched the draw with Premier League side Southampton.
And Sunderland, usually watched by more than 40,000 fans at the Stadium of Light, drew a crowd of just 17,632 for the 0-0 draw against Burnley.
However, non-league fans eager to witness an FA Cup upset travelled in big numbers to games.
Seventh-tier Stourbridge went into the third round as the lowest-ranked side left in competition and took more than 2,000 supporters to Wycombe, where an Adebayo Akinfenwa late winner sent the League Two side through.
"The FA Cup win will make a difference," said Stourbridge manager Gary Hackett. "Financially, it will put the club in a very strong position, and I think people will remember this day for a long, long time - albeit in defeat."
Eastleigh, meanwhile, had more than 1,500 supporters at Brentford - just 500 fewer than the National League side averages for home games.
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The draw for the FA Cup fourth round takes place on Monday, 9 January at 19:10 GMT.
It will be live on BBC Two and there will also be live text commentary on the BBC Sport website plus BBC Radio 5 live coverage.
The fourth-round ties will take place on the weekend beginning 28 January.
FA Cup third-round results:
West Ham United 0-5 Manchester City
Manchester United 4-0 Reading
Accrington Stanley 2-1 Luton Town
Barrow 0-2 Rochdale
Birmingham City 1-1 Newcastle United
Blackpool 0-0 Barnsley
Bolton Wanderers 0-0 Crystal Palace
Brentford 5-1 Eastleigh
Brighton & Hove Albion 2-0 Milton Keynes Dons
Bristol City 0-0 Fleetwood Town
Everton 1-2 Leicester City
Huddersfield Town 4-0 Port Vale
Hull City 2-0 Swansea City
Ipswich Town 2-2 Lincoln City
Millwall 3-0 Bournemouth
Norwich City 2-2 Southampton
Queens Park Rangers 1-2 Blackburn Rovers
Rotherham United 2-3 Oxford United
Stoke City 0-2 Wolverhampton Wanderers
Sunderland 0-0 Burnley
Sutton United 0-0 AFC Wimbledon
Watford 2-0 Burton Albion
West Bromwich Albion 1-2 Derby County
Wigan Athletic 2-0 Nottingham Forest (15:00)
Wycombe Wanderers 2-1 Stourbridge
Preston North End 1-2 Arsenal
Premier League sides Bournemouth, Stoke City and West Bromwich Albion were knocked out of the FA Cup by lower league opposition in the third round.