After a woeful start to the Premier League season, Tottenham's hopes of a morale-boosting cup run came to a dispiriting end at rain-lashed Anfield.
They were swatted aside by Liverpool, with Alexis Mac Allister, Cody Gakpo and Dominik Szoboszlai scoring for the Reds.
Roberto De Zerbi's fourth-bottom team are without a win or even a goal in their first four league matches, losing twice and drawing twice.
Tottenham's only win this season has come in the League Cup against second-tier Charlton.
After successive 17th-place finishes -- including avoiding relegation on the final day of last season -- the north London club spent over £300 million ($404 million) on 10 new signings since the end of last term.
But the return on that eye-watering investment has not been immediate, sparking fears of another relegation battle.
Adding to De Zerbi's problems, unsettled striker Richarlison took to social media to lament the Italian's decision to leave him out of the squad to face Liverpool.
Richarlison wants to leave but moves to Everton and Vasco Da Gama have fallen through recently.
Tottenham host Aston Villa on Saturday in a game that De Zerbi desperately needs to win to ease the pressure on him going into the international break.
Liverpool remain unbeaten at the start of the Andoni Iraola era, although they have won just once in four league matches.
Iraola made 10 changes but Liverpool went ahead after 21 minutes with a flowing move.
Gakpo picked out Rio Ngumoha and he teed up Mac Allister to blast a first-time finish past Martin Dubravka into the roof of the net.
Gakpo doubled Liverpool's advantage in the 54th minute, whipping a fine strike into the far corner.
Tottenham finally scored a goal against top-flight opposition this season -- albeit in a different competition -- when Conor Gallagher punished poor marking to net from a corner in the 69th minute.
But Szoboszlai rubbed salt into Tottenham's wounds in stoppage time with a 25-yard rocket.
Dowman makes his mark
At Portman Road, Dowman took centre stage to remind Arsenal manager Mikel Arteta of his burgeoning talent.
Arsenal, who lost the League Cup final against Manchester City last season, have won their six games in all competitions this term.
Arteta made nine changes from the side that won at Sunderland on Saturday, with 16-year-old Dowman given his first appearance this season.
Dowman has been earmarked as a future star since bursting onto the scene as a 15-year-old last season.
But Arteta is treating the midfielder with kid gloves, bringing him on slowly while the Premier League champions are thriving.
Dowman showed Arteta what he can add to the party in the seventh minute, flashing quick feet to skip past Cedric Kipre before slotting home with a composed finish.
It was Dowman's second goal for Arsenal after his strike against Everton in March.
Noni Madueke increased Arsenal's lead in the 16th minute, lashing a low shot past Christian Walton from just inside the penalty area.
Dowman struck again in the 47th minute, running onto Martin Zubimendi's pass and finishing with aplomb.
Mikel Merino grabbed Arsenal's fourth, curling home from Dowman's pass in the 58th minute.
Anis Mehmeti's 62nd-minute reply and Chuba Akpom's stoppage-time strike were little consolation for outclassed Ipswich.
Fulham made nine changes but still won 3-2 at Championship leaders West Ham, with goals from Rodrigo Muniz, Cesar Palacios and Oscar Bobb, who bagged the 78th-minute winner.
Brentford won 2-1 at third-tier Reading thanks to goals from Callum Wilson and Fabio Carvalho.
On Wednesday, Manchester United host Brighton, Aston Villa travel to Coventry and Everton face Wolves.
Holders Manchester City are at home to Norwich on Thursday.