FA Cup holders Arsenal beat Burnley 2-1 at the Emirates Stadium to book their place in the fifth round.
Arsenal, who won the competition in 2014 and 2015, handed Mohamed Elneny his debut and welcomed Alexis Sanchez and Francis Coquelin back into the starting lineup after spells on the sidelines through injury.
The Gunners took the lead on 19 minutes when Sanchez set up Calum Chambers to bend a shot into the top corner, but the Championship side hit back on the half-hour mark when Sam Vokes headed past David Ospina.
Sanchez restored their advantage early in the second half, crashing home Alex Oxlade-Chamberlain's cross, to secure progress.
Kelechi Iheanacho scored a hat trick as Manchester City thrashed Premier League relegation battlers Aston Villa 4-0 at Villa Park.
Iheanacho stabbed home the opener on four minutes after Villa keeper Brad Guzan had blocked Fernando's header.
The Nigerian doubled their advantage on 24 minutes, sending Guzan the wrong way from the penalty spot after Raheem Sterling went down in the area.
He added his third on 73 minutes following a poor backpass from Idrissa Gueye, and Sterling made it 4-0 moments later.
Liverpool's packed fixture slate will get even busier after a goalless draw with West Ham.
The result means the Reds' February schedule includes a replay in at Upton Park to go with three Premier League fixtures, a two-legged Europa League tie against Augsburg and the Capital One Cup final against Manchester City.
Liverpool came the closest to breaking the deadlock in the 75th minute, as West Ham keeper Darren Randolph made three saves in quick succession.
Randolph did well to keep out Christian Benteke, then Joe Allen and then Benteke again from close range.
Tottenham Hotspur eased into the fifth round with a 4-1 victory at Colchester United.
Colchester, who saw defender Alex Wynter stretchered off early on following a clash of heads and fellow centre-back Tom Eastman hurt in the same incident, fell behind on 27 minutes when Nacer Chadli fired home.
Spurs extended their lead through a deflected Eric Dier shot on 64 minutes before Marvin Sordell struck a post for the hosts. Chadli then headed home for his second of the game before Ben Davies scored an own goal shortly afterwards, making it 3-1.
Tom Carroll had the last word for the visitors, firing in off the underside of the bar from Chadli's cross.
Crystal Palace beat Stoke City 1-0 at Selhurst Park.
Wilfried Zaha put Palace ahead on 18 minutes, beating Stephen Ireland and Marc Wilson before sending the ball between keeper Jakob Haugaard's legs.
That proved enough to give the out-of-form Eagles a morale-boosting victory over the 2011 finalists.
West Bromwich Albion were held to a 2-2 draw by League One side Peterborough United after a flurry of late goals.
Saido Berahino gave West Brom the lead on 14 minutes, firing past Ben Alnwick from 25 yards after good work from Rickie Lambert.
Posh hit back through Shaq Coulthirst, a new signing from Tottenham, after a defensive mix-up on 79 minutes, but Berahino appeared to have settled it with a well-placed finish shortly afterwards.
On 86 minutes, though, Jon Taylor made it 2-2 to take the match to a replay.
Watford needed a late goal from Odion Ighalo to defeat Championship side Nottingham Forest 1-0 at the City Ground.
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