Sunderland v Manchester United
Manchester City v West Ham
First legs to be played week commencing January 6; second legs to be played week commencing January 20.
A review of Wednesday's Capital One Cup quarter-finals, including victories for West Ham and Manchester United.
Sherwood thought he had made a dream start to life in the dugout when Emmanuel Adebayor put Spurs in front midway through the second half, but Matt Jarvis scored 10 minutes from time and Modibo Maiga headed in an 85th-minute winner to send the Hammers, struggling in the Premier League, into the semi-finals.
The Hammers, who had won just two of the 10 matches between visits to White Hart Lane, had been blunt until exposing the defensive deficiencies which were all too evident all too often during Villas-Boas' reign, including in Sunday's 5-0 home loss to Liverpool.
Hammers boss Sam Allardyce knows Premier League results will determine his future, but a place in the last four and the prospect of a Wembley final could provide a much-needed fillip for his relegation-threatened side.
It had appeared Allardyce would have more immediate worries over his position when former West Ham striker Jermain Defoe crossed for Adebayor to net a thumping volley after 67 minutes. It was his first goal since the May win at Stoke.
The strikers - in particular Adebayor, who was making his first start of the season - were marginalised by Villas-Boas and provided an emphatic answer to their former boss.
But Adebayor ran out of energy and was replaced, Andros Townsend went off with a hamstring injury and West Ham struck twice late on to advance.
Ashley Young scored his first goal in over 19 months before setting up Patrice Evra to send Manchester United into the semi-finals with a 2-0 victory over Stoke at the Britannia Stadium.
Booed by the home fans for going to ground too easily, Young has never been a favourite of the United support either.
But they were happy to celebrate with the England winger on Wednesday night after he lashed home what turned into a lay-off by substitute Javier Hernandez from 20 yards.
Not since May 2012 had Young found the net.
And when he then threaded a pass through for Evra to score 12 minutes from time, the former Aston Villa man ensured David Moyes could still land the first silverware available to him in a competition he was beaten by United in the final of four seasons ago.
However, it was not all good news for United, who were without Wayne Rooney due to injury.
With Robin van Persie already sidelined for four weeks with a thigh strain, the prospect of also being without the man who has carried United through much of a troubled campaign is an unpalatable one given they have plenty of work ahead of them over a packed festive programme merely to force their way into top-four contention.