Bournemouth eased into the fourth round with a 4-0 win over Lincoln City at the Vitality Stadium, a Ryan Christie hat-trick and a late strike from Rayan giving Marco Rose his first competitive victory since taking charge.
The Championship visitors started brightly and had spells of the game in the opening exchanges, but faded badly as the tie wore on, allowing Bournemouth's superior quality to take over in the second half.
Crystal Palace were equally comfortable in a 3-0 win over Middlesbrough at Selhurst Park, with Jorgen Strand Larsen heading in twice either side of half-time before a sublime late finish from substitute Daichi Kamada completed the scoring. Head coach Pierre Sage made eight changes from Saturday's 3-2 win at Fulham, using the tie to hand first starts to summer signings Oscar Mingueza, Honest Ahanor and Dario Osorio as Palace eased through to the last 16 without needing to call on their strongest XI.
Sunderland booked their own place in the fourth round with a narrow 1-0 win over Hull City, Chemsdine Talbi scoring the only goal on his return to the side in a game short on clear-cut chances at either end.
Talbi had been left out of Sunderland's Europa League squad last week and has attracted reported interest from Saudi Arabia, making his contribution on the night a timely reminder of his quality to anyone weighing up a move for the winger.
Newcastle United needed a late intervention to see off a stubborn Millwall at the Den, Joe Willock turning in Lewis Hall's driven cross in the 81st minute to spare Matthias Jaissle's side a penalty shootout.
The Magpies named a strong team out of respect for their injury-hit Championship opponents and for the competition itself, but were largely blunt in front of goal until Willock's breakthrough.
The best chance of the night for the hosts fell to substitute Tairyk Arconte, whose drilled effort cannoned back off the post after he capitalised on slack defending from Tino Livramento to run through on goal, leaving Millwall to rue the missed opportunity as they exited the competition.