Zlatan Ibrahimovic and Anthony Martial scored twice as Manchester United crushed West Ham United 4-1 in the League Cup quarter-finals, while Arsenal were humbled by Southampton.
United manager Jose Mourinho served a one-game touchline ban after his dismissal for kicking a water bottle during Sunday's 1-1 Premier League draw against West Ham, but his absence had no ill-effects.
Ibrahimovic put United ahead in the second minute and although Ashley Fletcher equalised, Martial's second-half brace restored the hosts' control before the Swede added a fourth goal in added time.
"After the West Ham goal we had 10 minutes where we felt it deeply. West Ham's first shot, they equalise," said Mourinho, who has overseen United's worst start to a top-flight season since 1989.
"But in the second half we got the confidence to play and play beautiful, attacking football.
"Goals plus performance means the real happiness."
United will play Hull City in the two-legged semi-finals, while Southampton's reward for winning 2-0 at the Emirates Stadium was a last-four encounter with Jurgen Klopp's Liverpool.
The game at Old Trafford notably saw Bastian Schweinsteiger make his first appearance of the season for United as a late substitute.
The former Germany captain has only recently returned to the first-team squad after being frozen out by Mourinho and received a huge ovation as he came on.
West Ham had needed less than two minutes to take the lead in Sunday's game, but on this occasion United were the early birds.
Wayne Rooney's clever reverse pass picked out the advancing Henrikh Mkhitaryan and the Armenian's alert back-heel freed Ibrahimovic to lift the ball past West Ham goalkeeper Adrian.
West Ham levelled in the 35th minute with a bolt from the blue as David de Gea spilled Dimitri Payet's shot and former United youngster Fletcher tucked in his first senior goal in front of the Stretford End.
Fortunately for United, they started the second half as sharply as they had attacked the first, a move down the right culminating in Mkhitaryan squaring for Martial to sweep home.
- Stunned -
Gunners forward Lucas Perez hit the crossbar in the closing stages, but Watford held on for their first league victory at Arsenal since 1988.
Arsenal are nine points behind Chelsea in third place and Wenger said: "It was obvious we were not sharp enough. It looked mentally that we were not ready for the challenges.
"Everybody in the Premier League is strong physically and 90 percent (effort) is not enough."
Tottenham missed a chance to close the gap on Chelsea after being held to a dour 0-0 draw by struggling Sunderland.
Mauricio Pochettino's side, who lost England left-back Danny Rose to a first half injury, rarely got into top gear in their second successive draw.
Struggling champions Leicester crashed to a third successive league defeat as Sam Vokes' controversial strike gave Burnley a 1-0 win at Turf Moor.
Claudio Ranieri's team were shattered when Michael Keane nodded down for Vokes from a corner and the ball appears to hit the striker's hand before he lashed in from close range in the 87th minute.
Leicester, with just one win in their last eight league games, are now two points above the relegation zone.
"It was handball for everybody but not the referee. He didn't see it and we lost the match," Ranieri fumed.
Sam Allardyce celebrated his first league win as Crystal Palace manager at the sixth attempt as the lowly Eagles won 2-0 at Bournemouth.
Scott Dann's 46th minute tap-in from Damien Delaney's flick on put third bottom Palace ahead and Christian Benteke wrapped up the points in second half stoppage-time.
Fourth bottom Swansea boosted their bid for survival with a 2-1 win over Southampton at the Liberty Stadium.
Middlesbrough drew 1-1 with West Bromwich Albion at the Riverside Stadium.