Arsenal eased past second-tier Reading 2-0 with Alex Oxlade-Chamberlain scoring twice, while Newcastle United romped to a 6-0 win over 10-man Preston North End and Hull City won 2-1 at Bristol City in the League Cup.
Daniel Sturridge sent Liverpool into the League Cup quarter-finals and gave his manager a reminder of his talents with two clinical goals in a 2-1 win over Tottenham Hotspur on Tuesday.
The England striker has struggled to convince Liverpool boss Juergen Klopp this season, but he was a livewire all night at Anfield where his double put the hosts in charge before Vincent Janssen pulled a goal back with a penalty for the visitors.
Klopp's side are joined in the last eight by Arsenal, who eased past second-tier Reading 2-0 with Alex Oxlade-Chamberlain scoring twice, while Newcastle United romped to a 6-0 win over 10-man Preston North End and Hull City won 2-1 at Bristol City.
Leeds United beat Norwich City 3-2 on penalties, while the quarter-final lineup will be completed on Wednesday with three more ties including Manchester United hosting local rivals and holders City in the pick of the fourth round matches.
With no European football to occupy his squad this season, Liverpool manager Klopp raised a few eyebrows by making 11 changes to the side that beat West Bromwich Albion 2-1 in the Premier League on Saturday.
Spurs, who are midway through a run of seven games in 23 days and have the Champions League to worry about, had more justification for retaining only Eric Dier from the side that drew 0-0 with Bournemouth at the weekend.
Liverpool, record eight times League Cup winners and last season's beaten finalists, were ahead after nine minutes when Sturridge, who has started just two of their last six games in all competitions, showed predatory instincts to poke home.
While his work rate often comes under scrutiny, Sturridge's eye for goal has never been in doubt and when Marko Grujic's shot deflected into his path, he showed lightning reactions to beat Spurs keeper Michel Vorm to the ball.
"He did what he has to do. It was brilliant, he could have scored three or four," said Klopp, who regularly prefers Brazilian Roberto Firmino in attack in the Premier League.
Sturridge passed up two chances either side of halftime, but he made amends by doubling Liverpool's lead in the 64th minute. Georginio Wijnaldum played him through on goal and Sturridge squeezed his finish through Vorm's legs in front of the Kop.
It had been smooth sailing for Liverpool until that point but Lucas Leiva nibbled the heels of Erik Lamela to concede a penalty, which Janssen slammed home with 14 minutes remaining.
Alberto Moreno was then lucky to avoid conceding a second spot kick after tangling with Lamela again, but the match ended with Liverpool back on the front foot as Sturridge struck the crossbar and substitute Danny Ings had an effort saved by Vorm.
Arsenal, who are unbeaten in all competitions since the opening weekend of the Premier League season, were frustrated for large periods of the first half before Oxlade-Chamberlain put them ahead against Reading after 33 minutes.
He doubled the lead with 12 minutes left when he drove a shot from distance that was deflected in off a Reading boot.
Hull City took a two goal lead at second-tier Bristol City when Harry Maguire and Michael Dawson scored within four minutes either side of halftime before Lee Tomlin pulled back a stoppage-time goal for the hosts.
Newcastle thrashed Preston in an all-Championship battle with Serbia striker Aleksandar Mitrovic and Senegal's Mohamed Diame both scoring twice while Matt Ritchie netted a penalty and Ayoze Perez scored in stoppage time to round off the rout.
Ronaldo Vieira scored the winning penalty for Leeds United against Norwich City in another all second-tier contest after the match finished 1-1 at fulltime and 2-2 after extra time.
