Manchester United downed Stoke City 2-0 to reach the League Cup semi-finals on Wednesday, 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 January 6.
"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."
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.
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 10-minute delay.
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.
United put the game to bed in the 78th minute when Evra curled a fine shot inside the right-hand post.
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.
Interim coach Tim Sherwood picked an adventurous team with Emmanuel Adebayor sliding in to slam home a volley in the 67th minute.
West Ham levelled through Matt Jarvis in the 80th minute before Modibo Maiga completed West Ham's comeback five minutes later with a header to give Sam Allardyce's side a second consecutive win at White Hart Lane following a 3-0 league success in October.