Also in the draw are seventh-tier side Harborough Town, who made history by making it into the first round for the first time, beating Bury 1-0 in the fourth qualifying round.
Ben Stephens squeezed the ball past Bury goalkeeper Mitch Allen from the penalty spot in the second half.
Harborough, who play in the Southern League Premier Division Central, had previously made the second qualifying round in both of the past two seasons.
National League South side Chesham United surprised Yeovil Town of the National League to go through to round one for the second term running.
Jack Cawley’s back-post header – the only goal of the game – sparked great celebrations at The Meadow.
Elsewhere, 10-man Aldershot Town left it until the 98th-minute to seal a 2-1 victory over National League South side Bath City.
The winning strike came from academy graduate Maxwell Mullins, who fired in his first goal for the club, following Christian Maghoma’s red card for a high challenge.
There was similar full-time joy for Southend United, who scored in the 93rd minute in their game at Eastleigh.
Substitute Aribim Pepple powered through the home side’s defence, before his shot narrowly evaded the grasp of Spitfires goalkeeper Joe McDonnell.
Fellow National League side Barnet progressed more comfortably, thumping Chelmsford City 4-0.
Callum Lee Stead netted twice from close range in the first half for the Bees.
Rochdale also scored four as they enjoyed a comfortable 4-1 win at fellow fifth-tier side AFC Fylde, who had former England and Sunderland striker Kevin Phillips in charge for the first time.
York City’s Ollie Pearce was another player to get a brace as they progressed with a 3-1 victory at eighth-tier side Biggleswade.
It was the same final score as Sutton United beat Chertsey Town – but the Southern League side missed a penalty when it was 2-1 which would have levelled the tie.
Meanwhile, Braintree Town got the better of Bishop’s Stortford in a scrappy affair at Cressing Road that saw Iron striker Inih Effiong slot the ball in the bottom corner for the only goal.
