Chelsea booked their spot in the fourth round after a comfortable 5-1 win over fifth-tier side Chesterfield at Stamford Bridge.
Timo Werner, Callum Hodson-Odoi, Romelu Lukaku and Andreas Christensen all netted in the first stanza before Hakim Ziyech made it 5-0 early in the second stanza.
Akwasi Asante scored the consolation goal for Chesterfield ten minutes before time.
Leicester City cruised to the fourth round after thrashing Watford 4-1 at the King Power Stadium.
Youri Tielemans gave City an early lead before James Maddison doubled their lead in the 25th minute.
Joao Pedro pulled a goal back for the Hornets but the floodgates opened thereafter, as Harvey Barnes and Marc Albrighton got two goals for the Foxes in the second stanza.
Everton booked their spot in the fourth round after edging second-tier side Hull City 3-2 in extra-time at KC Stadium.
Tyler Smith gave Hull a dream start with the opener within the first minute but Demarai Gray equalised for the visitors in the 21st minute and Andre Gomes gave the Toffees a 2-1 lead ten minutes later.
However, Ryan Longman levelled matters for the hosts in the last 19 minutes, forcing the game into extra-time.
Andros Townsend found the winner for Everton in the ninth minute of extra-time.
Brighton and Hove Albion needed extra-time to reach the fourth round after edging Championship side and ten-man West Bromwich Albion 2-1 at The Hawthorns.
After a goalless first stanza, Callum Robinson eventually broke the deadlock for West Brom early in the second stanza but the hosts were down to ten men in the last 21 minutes after Cedric Kipre got a second booking and was sent off.
That allowed Jakub Moder to force the game into extra-time with the equaliser for Brighton nine minutes before time and Neal Maupay netted the winner in the eighth minute of extra-time.
Ten-man Southampton are through to the fourth round after needing extra-time to edge Championship side Swansea City 3-2 at Liberty Stadium.
Nathan Redmond gave the Saints an early lead but the visitors were down to ten men on the half-hour mark after Yan Valery was red-carded and Joel Piroe found the equaliser for Swansea 13 minutes before time, as the sides went to extra-time.
Jan Bednarek's own goal early in extra-time gave City a 2-1 lead but Mohamed Elyounoussi quickly levelled matters and Shane Long got the winner for the Saints with eight minutes remaining of extra-time.
Brentford comfortably booked their spot in the fourth round after a resounding 4-1 win over League Two side Port Vale thanks to a hat-trick by Bryan Mbeumo at Vale Park.
Marcus Forss broke the deadlock for the Bees in the 26th minute while Mbuemo netted his hat-trick in the second stanza.
Kian Harratt scored what proved to be a consolation goal for Port Vale in the second stanza.
Newcastle United were dumped out in the third round after a narrow 1-0 defeat to League One side Cambridge United at St. James' Park.
After a goalless first stanza, Joe Ironside scored the famous goal for Cambridge four minutes before the hour-mark that eventually took them to the fourth round.
