In a game that saw Jay Rodriquez score twice, the game however was overshadowed by the video assistant referee (VAR).
After West Brom led 2-1 early in the first half, it appeared that West Brom had extended their lead, only before having it chalked off by the VAR.
Following this, the first ever on field referee review was used minutes later, as the referee used it to award Roberto Firmino a penalty, which consequently went on to hit the cross bar.
Later on in the half, West Brom had a pinch of luck with the VAR, which confirmed they had gone 3-1 up just before the half after a long deliberation from the VAR.
After the half-time interval, a Mo Salah goal wasn’t enough to overcome a defiant West Brom side, which became the first team to win at Anfield since April last year.
In a match that saw Alexis Sanchez make his Manchester United debut, the Red Devils saw off minnows Yeovil Town 4-0 in a one-sided contest.
It was evident however in the first half that Sanchez lost possession too often and easily, yet he was still able to provide assists for Marcus Rashford and Ander Herrera’s goals in a mixed but solid debut game for the star signing.
Elsewhere, Tottenham survived a huge scare at lowly Newport, coming out with a 1-1 draw to force a replay at Wembley Stadium.
With the 4th division side scoring in the 44th minute, a Harry Kane equaliser with eight minutes to play saved them from an embarrassing result.
Premier league giants Chelsea easily accounted for Newcastle 3-0, while a sublime free kick from Kevin De Bruyne saw Manchester City beat Cardiff City 2-0.
In another upset of the round, West Ham bowed out of the Cup to second division side Wigan Athletic 2-0, with the Hammers failing to register a shot on target.
In other games, Brighton and Hove Albion struck late thanks to a 90th minute strike from Glen Murray to defeat Middlesborough 1-0, while a Premier League encounter between Southampton and Watford saw the Saints prevail 1-0 thanks to an early strike from Jack Stephens in the 4th minute.
Relegation battlers Swansea City again struggled, drawing 1-1 to League Two side Notts County.
The 5th round draw of the FA cup will be drawn in the early hours of Tuesday morning.