Manchester United beat Stoke City 2-0 to reach the League Cup semi-finals, while the post-Andre Villas-Boas era at Tottenham Hotspur began with defeat by West Ham United.
After a first-half hailstorm briefly forced the teams off the pitch at the Britannia Stadium, United prevailed through fine strikes from Ashley Young and Patrice Evra.
Their reward was a semi-final tie against Sunderland, 2-1 victors over Chelsea on Tuesday, while West Ham will play Manchester City, with the first legs of both ties due to be played in the week beginning 6 January.
"The first goal tonight, whoever got it was going to make a big difference," United manager David Moyes told Sky Sports.
"It was a tight game. We had some good play at times. We hadn't created too many chances, but I didn't think Stoke City created too many chances either."
On the prospect of facing Sunderland, he added: "It's a cup game. It shows you how well Sunderland played -- they beat Chelsea last night and they played well to get that result.
"They've got a new manager (Gus Poyet) as well, so a lot of things can happen between now and then, but obviously we're just really pleased that we got ourselves into the semi-final."
With Wayne Rooney absent due to an unspecified injury, Moyes deployed Danny Welbeck as a lone striker, while Chris Smalling, Anderson and Young were all brought into the team.
Young was given an early sight of goal when a square pass from Welbeck found him in space on the edge of the box, but he could only find the side-netting with his rising shot.
The hail arrived in the 28th minute, sending players and match officials scurrying for the cover of the changing rooms, before play resumed following a ten-minute delay.
Jonny Evans might have put United ahead shortly before half-time but he could not get a shot away after latching onto Smalling's near-post flick-on.
Moyes introduced Javier Hernandez with just over half an hour remaining and moments later Young made the breakthrough in stunning fashion.
The former Aston Villa winger played a pass forward to Hernandez and when the ball came back to him on the edge of the box, he met it with a first-time drive of searing power that Thomas Sorensen got his gloves to but could not stop.
Stoke rallied, briefly, but United put the game to bed in the 78th minute when Evra exchanged passes with Young before curling a fine shot inside the right-hand post with his seldom-used right foot.
West Ham in comeback win at Spurs
Playing for the first time since Villas-Boas was sacked on Monday, Spurs let a 1-0 lead slip in a 2-1 loss at home to London rivals West Ham.
Villas-Boas's departure appeared to have caught the producers of the Tottenham match-day programme by surprise, with the Portuguese still listed as "Head Coach" on its back page.
Interim coach Tim Sherwood picked an adventurous team, giving Emmanuel Adebayor his first start of the season alongside Jermain Defoe up front, and the pair combined to give Spurs the lead in the 67th minute.
Defoe crossed from the left and Adebayor slid in to slam home an emphatic volley via the underside of the crossbar.
However, there was a blow for Spurs when Andros Townsend was forced off with an apparent hamstring injury and in the 80th minute West Ham levelled when Matt Taylor teed up Matt Jarvis to beat Hugo Lloris at his near post.
Modibo Maiga completed West Ham's comeback five minutes later, heading in a Mohamed Diame cross to give Sam Allardyce's side a second consecutive win at White Hart Lane following a 3-0 league success in October.
Maiga almost made it 3-1 in stoppage time but his drive from 20 yards came back off the bar.
"This is a major disappointment tonight, for myself, for the boys and the football club," Sherwood, a former Spurs midfielder who was previously working as the club's technical coordinator, said.
On his chances of holding onto the role on a permanent basis, he said: "I haven't spoken to the chairman (Daniel Levy).
"We have to have a chat and see. It has to fit me and the club."
League Cup semi-final draw:
Sunderland v Manchester United
Manchester City v West Ham United
First legs to be played during the week commencing 6 January; second legs during week commencing 20 January.