Chelsea conceded late goals in both normal time and extra time to lose 2-1 to Sunderland in the League Cup quarterfinals on Tuesday, while Manchester City also advanced thanks to Edin Dzeko's double at Leicester.
South Korea midfielder Ki Sung-yueng grabbed Sunderland's winner with two minutes left at the Stadium of Light, with Chelsea having been taken to extra time after conceding an 88th-minute equalizer by Fabio Borini.
"Football is about scoring goals and winning matches, not being the best team on the pitch," said Chelsea manager Jose Mourinho, whose largely second-string side wasted a number of chances after Frank Lampard bundled in the opening goal in the 46th.
Like Chelsea, City rested several key players but still had enough to see off second-tier Leicester 3-1, with Dzeko's brace adding to the opener scored by Aleksandar Kolarov from a superb free kick.
Dzeko has been given limited playing time in recent weeks because of the brilliant form of fellow strikers Sergio Aguero and Alvaro Negredo. With Aguero sidelined for at least a month with a calf injury, Dzeko is set to see more action over the busy Christmas period.
In making it to the semifinals for the third time in five years, City took its goal tally for the season to 75 from 25 games.
"It is an important competition," City manager Manuel Pellegrini said. "It is important to win every game you play in and to get to the final at Wembley would be wonderful for the supporters."
The only negative of the evening for City was the sight of right back Pablo Zabaleta hobbling off in the first half, clutching his right hamstring. City's other right back, Micah Richards, is already out injured.
City hasn't reached the League Cup final since winning the competition in 1976. It lost the FA Cup final to Wigan last season.
The other quarterfinals take place on Wednesday, when managerless Tottenham hosts West Ham and Manchester United visits Stoke.
Chelsea was minutes away from a place in the last four after Lampard was on the right end of a goal-line decision.
The veteran midfielder was famously denied a legitimate goal in a World Cup second-round match between England and Germany in 2010 when his shot hit the bar and bounced over the line, only for officials to miss it. Goal-line technology was introduced by FIFA largely as a result of that incident.
On this occasion, referee Anthony Taylor pointed to his watch to indicate that the Goal Decision System -- used on Tuesday for the first time in an English cup match -- had approved the goal after the ball had rolled in off a combination of Lampard and the retreating Lee Cattermole.
Chelsea has had problems finishing off opponents this season and Samuel Eto'o was guilty of wasting a great chance before Borini drove a shot through David Luiz's legs on the goal-line after Jozy Altidore's initial shot was saved.
Sunderland, which is last in the Premier League, was the better team in extra time and after Ki had a header brilliantly saved by Mark Schwarzer, the South Korean cut inside and buried a low shot into the corner just as penalties were looming.
"We always wanted to go through in this competition but it wasn't a priority," Mourinho said.