However, both accomplishments were overshadowed by the collapse of Bolton player Fabrice Muamba during a game Saturday.
Torres scored twice in a 5-2 win over Leicester and Chelsea will now face the winner of the Tottenham-Bolton quarter-final, which was abandoned Saturday after Muamba suffered cardiac arrest on the field.
The Bolton midfielder remained in critical condition Sunday in intensive care and there was concern throughout the soccer community.
After Gary Cahill opened the scoring for Chelsea, the defender raised his jersey to reveal a "Pray 4 Muamba" T-shirt in tribute to his former Bolton teammate.
"It was a very difficult day for him and the whole football community, all our thoughts are with Fabrice," Chelsea manager Roberto Di Matteo said.
Liverpool, which won the League Cup last month, beat Stoke 2-1 to secure a potential semifinal derby if Everton can overcome Sunderland in a replay.
In the Premier League, Manchester United thrashed 10-man Wolverhampton Wanderers 5-0 to move four points ahead of Manchester City, which has a game in hand.
"The important thing was for us to do our job. There are nine games left and we have to keep whittling them down," United manager Sir Alex Ferguson said. "Eventually the games run out and hopefully we will achieve what we want."
The Premier League is all the defending champions have left to win this season, while Chelsea — languishing in fifth place — is in the Champions League quarter-finals and now a domestic semifinal.
The win over Leicester extended Di Matteo's winning run to four matches since replacing Andre Villas-Boas to become interim manager two weeks ago.
And Torres finally scored for the first time in 25 hours 41 minutes by squeezing Raul Meireles's pass into the corner in the 67th minute at Stamford Bridge.
The Spain striker added another goal in the 85th off a header from Meireles's corner.
"I needed those goals. I've been working so hard to get them," Torres said. "Maybe the job of a striker is to score goals, and if you don't do it people think you're playing badly.
"But the support has been here and I feel the confidence of the manager (Roberto di Matteo) now. We have some important games coming."
After Cahill's opener, Salomon Kalou found the net in the 17th with a neat finish. Meireles rounded off the win in stoppage time after Torres' double. Jermaine Beckford and Ben Marshall grabbed consolation goals for second-tier club Leicester.
At Anfield, Luis Suarez put the hosts ahead in the 23rd minute and, although former Liverpool striker Peter Crouch tied it quickly, Stewart Downing's second goal of the season in the 57th knocked out last year's runners-up.
Downing collected the ball in the inside-right channel, and after fortuitously having it returned to him via Steven Gerrard's backheel, he continued to the edge of the area before drilling a fierce left-footed shot into the net.
"It's never easy against a tough physical side like Stoke," Gerrard said. "Today we got the luck and Stewart took his goal fantastically well, and off we go to Wembley for the second time."
A cup double would make amends for Liverpool's league woes, with Kenny Dalglish's side seventh in the standings.
Man United, though, appears to be on course for a record 20th league title.
A fifth straight league win for the defending champions was started by Jonny Evans scoring his first United goal in the 21st minute as Wolves sunk to bottom place.
After Wolves defender Ronald Zubar was dismissed in the 40th after receiving a second yellow card, Antonio Valencia and Danny Welbeck extended United's lead before the halftime. Javier Hernandez scored twice after the break.
Newcastle strengthened its grip on sixth place with a 1-0 victory over Norwich, with Papiss Demba Cisse's 11th-minute strike securing a first win in five league games for the hosts.