Fabled FA Cup giantkillers Hereford booked themselves a third-round date in January by beating Coca-Cola League One side Port Vale 4-0 at Edgar Street.
The Bulls, famously knocked out top-flight Newcastle in 1972 in a classic FA Cup upset, raced to victory with goals from Luke Webb (41), a two-minute double from Robert Purdie and one from Andy Ferrell in the 83rd minute.
League Two Barnet also secured a comfortable victory over a team from the league above them, hammering Northampton 4-1 at Underhill.
The Londoners fell behind to a Scott McGleish goal on the stroke of half-time, but the hosts came thundering back.
Adam Birchall (49) equalised and four minutes later Dean Sinclair headed in from a Jason Puncheon cross.
Ian Hendon blasted in a penalty (65) after David Hunt fouled Puncheon, before Magno Vieira made sure with an 87th-minute goal.
Swindon, second in League Two, sneaked past Conference side Morecambe thanks to Christian Roberts' 89th-minute penalty.
League Two Wrexham knocked out Scunthorpe from the league above, claiming a 2-0 win at Glanford Park.
Mark Jones (49) set the Welsh side on the path to victory and Kevin Smith made it safe (66).
League Two Peterborough were shock 2-1 victors at League One Tranmere, the Posh winning thanks to a Danny Crow double.
Basingstoke from the Nationwide Conference South remain in the competition after a 1-1 draw at Aldershot, who play a league above them.
Basingstoke led through Joe Bruce's 45th-minute goal but John Grant equalised for Aldershot.
Tamworth from the Conference reached the third round after winning 2-1 away to league rivals Rushden & Diamonds.
Conference side Stafford were beaten 3-0 at Brighton. Dean Hammond's cross-shot put the Seagulls ahead (18), Alex Revell headed in a second (66) and Jake Robinson sealed the victory in the final minute.
Bristol Rovers and Bournemouth must play again after a 1-1 draw, while Mansfield drew 1-1 at home to League One Doncaster. It took a last-minute goal from Brian Stock to earn the visitors a replay.
League Two's bottom club Macclesfield, bossed by Paul Ince, won 2-1 at home to Hartlepool, while Bury drew 2-2 at home to Chester.
Swansea came from behind to win 3-1 at Darlington while Blackpool made their League One superiority count in a 2-0 win at MK Dons.
Torquay earned a replay against League One's bottom club Leyton Orient, drawing 1-1 at Plainmoor.