Leeds will launch their defence of the Ladbrokes Challenge Cup against fellow Super League strugglers Huddersfield.
The Rhinos beat the Giants in a sixth-round tie at Headingley on their way to successfully defending the trophy last year but this time will have to travel to the John Smith's Stadium.
The two sides, currently in the bottom three of Super League, will have a dress rehearsal for the tie when they meet in a league match at the same venue on Friday week.
The sixth-round draw, made on BBC Radio 4's Today programme by presenter John Humphrys and cup winner Martin Offiah, threw up just two other all-Super League ties.
Castleford will be at home to Salford in a repeat of the 1969 Wembley final while Hull will visit St Helens.
The two French clubs were both handed away ties, with Catalans Dragons going to John Kear's Batley and Wakefield hosting Toulouse, the League One club who knocked out Championship leaders Leigh in Saturday's fifth-round tie.
Oldham's reward for putting out Hull KR is a home tie against Warrington while Halifax will host Widnes and Wigan go to Dewsbury in a repeat of the sixth-round tie in 2014 which they won 58-6.
Oldham coach Scott Naylor wanted a money-spinning away tie but was delighted to draw Super League leaders Warrington at home.
"I'm really happy with that," Naylor said. "It will be really good for the lads to play against a high-quality Super League team that is flying this year.
"It will be nice for some of my lads to see Stef Ratchford and people like that who they played with in the academy at Salford.
"It's a good draw and, like we did against KR, we will go and give everything we've got. It's obviously another enormous challenge for us.
"We've got two really important games in the next couple of weeks to play but we'll be looking forward to that. Hopefully, a really big crowd turns up and the club gets a decent pay day out of it."
The Roughyeds were forced to move out of their tiny Whitebank Stadium after gaining promotion from League One at the end of last season because it failed to meet minimum standards for the Championship and Naylor is hoping the club can go some way to filling the 6 ,500-capacity Bower Fold, the ground they share with Stalybridge Celtic.
"Stalybridge is a great ground, a fantastic place and so far this season it's been good for us," Naylor said.
"We've won four games there already so for us it feels comfortable, even though we've only been there this season. It feels like we've been there for a long time.
"They make us very welcome and I'm sure Warrington will enjoy the pitch which is amazing but it's our own ground so we've got to make it a fortress."