The FA Cup's lowest-ranked team Warrington Town have been drawn against Conference high-flyers Gateshead in the second round.
Conference North Worcester, who beat Coventry on Sunday, will travel to another League One side, Scunthorpe.
Northern Premier outfit Blyth Spartans, who reached the fifth round in 1978, are at fellow North East side Hartlepool United of League Two.
The ties will be played on 5, 6, 7 and 8 December.
Of the nine non-league sides definitely through to the second round, eight of them are drawn to play away from home.
Chester and Dartford have tricky away trips to League One sides, visiting Barnsley and Bradford respectively, while Dover head to League Two Cheltenham.
Warrington boss Shaun Reid, whose eighth-tier side beat Exeter on Friday, told BBC Sport: "Gateshead are doing very well in the Conference [currently third]. It will be a difficult tie, but it's the FA Cup and it's 11 v 11.
"We won't go there with fear. The FA Cup seems to bring the best out of my players.
"I've got plenty of people in football who can help us scout - I'll call in a few favours. They'll find it more difficult to find out about us - I change my team a lot."
Worcester City's reward for causing possibly the biggest shock of the round is their trip to Scunthorpe, who are currently fourth from bottom in League One.
Worcester manager Carl Heeley said: "It's another tough draw for us on the road again.
"But we're just delighted to be here and give a good account of ourselves. We're in the draw and we've got every chance."
Blyth Spartans - in the seventh tier - carry an FA Cup giant-killing reputation into the second round. Thirty-six years ago they defeated second-tier Stoke City before going out to Wrexham in a fifth-round replay.
The Northumberland outfit eased past Conference Premier club Altrincham 4-1 to reach the second round for the first time since 2008-2009. They now face Hartlepool, who are bottom of League Two.
"It's the fifth away game in six in the Cup. It's a good game. I know [manager] Paul Murray and a couple of lads that play for them," said Blyth manager Tom Wade.
"They have a young side like us. It's a good tie and local for us. It's going to be a great game. We'll have a lot of supporters there."
Elsewhere, three non-league sides face trips to League One clubs.
Conference South Basingstoke or Conference Premier Telford will fight it out in their replay for the right to play at leaders Bristol City.