The fifth round got under way with Liverpool defeating Wolverhampton Wanderers 3-1, thanks to second-half goals from Andy Robertson, Mohamed Salah and Curtis Jones.
League leaders Arsenal secured their place in the quarter-final after they beat League One side Mansfield 2-1 thanks to goals from Noni Madueke and Eberechi Eze.
Chelsea came from behind twice to beat 10-man Wrexham in a six-goal thriller, with Alejandro Garnacho and Joao Pedro's goals in extra-time securing the win for the Blues.
Omar Marmoush scored against Newcastle United once again as Manchester City came from behind to book their spot in the next round.
Fulham bowed out to Championship side Southampton on Sunday. The tie had looked to be heading to extra time, but Fulham's Joachim Andersen caught Finn Azaz in the penalty area and Ross Stewart blasted home the resulting spot-kick in the first minute of stoppage time.
Sunderland were also eliminated by lower league opposition on Sunday, following a 1-0 defeat to Port Vale of League One, but Leeds United made it through to the last eight with a 3-0 victory over Norwich City. Sean Longstaff, Gabriel Gudmundsson and Joel Piroe were the goalscorers at Elland Road.
The last all-Premier League tie of the fifth round saw West Ham United defeat Brentford on penalties at the London Stadium.
Friday 6 March
Wolves 1-3 Liverpool
See: Wolves report | Liverpool report
Saturday 7 March
Mansfield Town 1-2 Arsenal
See: Arsenal report
Wrexham 2-4 Chelsea
See: Chelsea report
Newcastle 1-3 Man City
See: Newcastle report | Man City report
Sunday 8 March
Fulham 0-1 Southampton
See: Fulham report
Port Vale 1-0 Sunderland
See: Sunderland report
Leeds United 3-0 Norwich City
See: Leeds report
Monday 9 March
West Ham 2-2 Brentford (5-3 pens)
See: West Ham report
FA Cup round dates
Quarter-final: Saturday 4 April
Semi-final: Saturday 25 April
Final: Saturday 16 May
For revised dates and kick-off times, click here.
The FA Cup winners will qualify automatically for the UEFA Europa League.