Championship side Barnsley have been rewarded for their stunning FA Cup win at Liverpool with a quarter-final tie at home to holders Chelsea.
League One side Bristol Rovers have been drawn at home against West Brom and in the only all-Premier League tie, Manchester United entertain Portsmouth.
In the other sixth-round contest, Championship side Cardiff City travel to Premier League Middlesbrough.
The games will be played on the weekend of 8 and 9 March.
Barnsley boss Simon Davey admitted the Tykes had their dream draw after being paired with Avram Grant's Chelsea.
"It's typical that we drew another Premier League team"
"It is a fantastic draw and a fantastic achievement for us to be here - and now we have a glamour tie as our reward," said Davey.
"We have a world-renowned team with some of the best players in the world coming here and it is one to look forward to.
"We have to make sure that this place is a cauldron for them and I am sure it will be packed. Hopefully we can put on a show for our supporters."
Bristol Rovers midfielder Chris Lines admits he cannot wait for the club's first FA Cup quarter-final since 1958.
"All the lads will be happy with a home draw and so will the club. We are all looking forward to it," Lines told BBC Radio 5 Live.
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"The pitch isn't in the best condition but it's a real leveller when teams from higher leagues come down here - we've proved that against Fulham and Southampton.
"We've had some experience of playing at Wembley in last season's play-offs but this would be even more of a fairytale to get to an FA Cup semi there."
Manchester United have now been drawn against Premier League opposition in their last 11 FA Cup draws - their 3-0 win at Wolves on 20 January 2006 the last time they played a lower league side in the competition.
"It's typical that we have another Premier League team," said Ferguson. "But it's a home draw, so it doesn't matter who you get.
"The good thing about the FA Cup is that the opposition bring an increased number of supporters, which makes for a great atmosphere."
Full draw for FA Cup quarter-finals:
Middlesbrough v Cardiff City
Manchester United v Portsmouth
Bristol Rovers v West Brom
Barnsley v Chelsea
Matches to be played on the weekend of 8 and 9 March.
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