Manchester United edged past Wolverhampton Wanderers and into the fourth round thanks to a divine Juan Mata winner.
Wolves thought they had taken the lead when Pedro Neto had the ball in the back of the net but the goal was disallowed following a VAR check for handball in the build up.
The visitors did eventually get the breakthrough when Anthony Martial put Mata through on before the Spaniard to calmly dinked the ball over the onrushing John Ruddy to seal a 1-0 win.
League Two outfit Carlisle took the lead via Nathan Thomas before centre-back Aden Flint scored either side of a Josh Murphy volley to put the visitors back in command.
But Harry McKirdy converted Thomas' low cross to keep things close before Danny Ward's fine turn and finish put a two-goal gap back between the sides and McKirdy scored again as Carlisle's final act in the competition.
And on Tuesday night, it was Tottenham Hotspur who ensured a safe passage to the fourth round, with a 2-1 win in their replay against Middlesborough.
Boro keeper Tomas Mejias gifted Spurs their opener when his pass was picked off by an onrushing Giovanni Lo Celso, who buried a shot into the bottom corner with just two minutes played.
Erik Lamela then produced an impressive slaloming run before finishing with the outside of his left boot before Jonathan Woodgate's side set up a nervy finish when George Saville pulled one back late on.
But Jose Mourinho maintained his record of never having lost in the third round of the Cup to set up an all-Premier League tie at Southampton in the next round.
Fellow top flight outfit Newcastle United ended Rochdale's memorable Cup run at St James' Park with a convincing 4-1 victory.
The Dale didn't give themselves the best start when Eoghan O'Connell turned Matt Ritchie's low cross into his own net but Newcastle soon found their rhythm to run out worthy winners.
Two further strikes from Matty Longstaff and Miguel Almiron gave the Toon a three-goal advantage at half time before Joelinton added a fourth and M.J Williams grabbed a late consolation for the visitors.
Newcastle now face a fourth round home tie against another League One opponent in Oxford United.
It will be Shrewsbury Town who welcome Liverpool to New Meadow in the next round, after a last-minute winner saw them edge past Bristol City 1-0.
The Shrews made the fourth round in consecutive seasons for the first time since 1983-84, and it came courtesy of a low-drilled Aaron Pierre strike with just a minute to spare.
Elsewhere Coventry City overcame fellow League One rivals Bristol Rovers with a comfortable 3-0 win to set up a home clash against Birmingham City in the next round. This tie will also have the unique situation of Birmingham fans being the away supporters at their own stadium, with Coventry currently ground sharing at St. Andrews.
Callum O'Hare picked out Maxime Biamou with a lovely through ball to open the scoring after just four minutes, before Josh Pask sandwiched a strike between a second Biamou goal to round things off.
And goals from Lucas Boye and Jordan Obita saw Reading move past Blackpool by 2-0, with their fourth round opponents yet to be decided from the replay between Carlisle and Cardiff City.
Meanwhile, Prenton Park was waterlogged meaning that Tranmere Rovers' home replay against Watford has been rescheduled for Thursday 23 January. The winners of that fixture will face Manchester United or Wolves in the fourth round.