Holders Chelsea will face Liverpool at Stamford Bridge in the quarter-finals of the Carling Cup after today's draw.
Avram Grant's side needed two late goals to scrape past Coca-Cola Championship side Leicester 4-3 in midweek while Liverpool beat Cardiff 2-1 at Anfield.
In-form Blackburn, whose fourth-round win at Portsmouth was their seventh straight victory in all competitions, are at home to Arsenal while Manchester City take on Tottenham.
New Spurs boss Juande Ramos saw his side beat Blackpool 2-0 at White Hart Lane in midweek in his first match in charge.
Those three ties will take place in the week commencing December 17 while the tie between West Ham and Everton will be played in the week commencing December 10.
The two sides are also scheduled to meet in the Barclays Premier League at Upton Park on December 15.
Draw for the Carling Cup Quarter Finals:
West Ham v Everton
Man City v Tottenham
Chelsea v Liverpool
Blackburn v Arsenal
West Ham v Everton to be played week commencing December 10
Manchester City v Tottenham; Chelsea v Liverpool; Blackburn v Arsenal to be played week commencing December 17.