Vanarama National League club Hartlepool United were knocked out 2-1 at home against National League North side AFC Telford United.
A goal in each half from the visitors` Amari Morgan-Smith and Daniel Udoh saw the Bucks progress into the next round.
Myles Anderson grabbed a late 93rd minute consolation for Pools.
Telford`s league rivals Blyth Spartans were also triumphant at Croft Park against National League opposition in Boreham Wood.
A thunderous 26th minute effort from Dan Maguire – his 150th goal for Spartans – appropriately proved to be the winner.
The holders Brackley Town are through.
They ended National League North rivals Hereford FC's six-game unbeaten run at home to run out 3-1 winners.
Brackley opener came from the penalty when Jordan Cullinane-Liburd was penalised for an infringement on the edge of the box. The referee immediately pointed to the spot and Shane Bryrne dispatched the spot-kick past Matt Yates.
Lee Ndlovu netted the second a minute into the second half - Matt Lowe swung in a cross from the left, and Ndlovu slid the ball home at the back-post.
In the 65th minute another good cross from left-back Lowe found Shaun Jeffers in front of goal, and he slotted the ball home.
Josh Gowling scored a stoppage time header in reply.
Other National League sides through include Chesterfield, who left it late, but a Tom Denton goal handed John Sheridan victory in the first game of his second stint as manager against Evo-Stik Southern League Division One Central side Bedford Town.
The striker, on as a second half sub, fired in an 89th minute winner against the Eagles to send the Spireites into the next round.
A solitary strike from Jack Richards was enough to see Maidstone United edge past National League South side Oxford City.
The only goal came on 36 minutes, Jack Paxman put the ball into the area and Richards arrived to fire the ball past the stranded Craig King.
Barnet progressed through following a 2-1 win over Southern League Premier Division South side Dorchester Town at The Hive.
The Bees broke the deadlock 5 minutes into the second half.
Shaq Coulthirst latched onto a ball over the top by Charlee Adams, setting himself before slotting low past the keeper.
It was all-square in the 72nd minute, Barnet failed to deal with a good cross in, it was headed back across goal and Ben Seymour made no mistake from close range.
The winner came 8 minutes from time when a great cross from the left by Elliott Johnson was powerfully headed home by Craig Robson.
AFC Fylde also scraped through at Mill Farm against Southern League Premier Division Central visitors Biggleswade Town.
A dogged display from the Waders came to nothing in the end as a 42nd minute effort from Nick Haughton from 25 yards won it for the Coasters.
In all-National League ties, Harrogate Town came from behind to win 2-1 at Crabble against Dover Athletic.
Visiting top scorer Jack Muldoon was the man who sent them packing, instantly cancelling out Inih Effiong's 14th minute strike before claiming the winner midway through the second penalty.
Goalkeeper Mitch Walker had earlier kept out a 5th minute spot-kick from Mark Beck who had been clipped by young midfielder Joe Bedford in the box.
Wrexham suffered a 1-0 home defeat to title-rivals Leyton Orient.
The game took a while to get going with little incident in the opening exchanges, but Wrexham almost took the lead with the first chance in the 17th minute.
The ball was played to Luke Summerfield who struck the post from 25 yards out.
But Wrexham fell behind in the 63rd minute after Mark Carrington was adjudged to have brought down James Brophy in the area, Matt Harrold converting the resulting penalty.
Orient were reduced to ten-men in the 79th minute when Myles Judd was shown a second yellow card following a foul on sub Rekeil Pyke but they held firm to go through.
Salford City saw off Dagenham & Redbridge at the Peninsula Stadium.
The Ammies took the lead when an error from Kenny Clark in the 33rd minute was pounced on by Kieran Glynn, who set up Adam Rooney to fire past Daggers` keeper Elliot Justham from close range.
And the hosts made sure 7 minutes from time when Danny Lloyd broke down the flank, before teeing up Mani Dieseruvwe to score.
FC Halifax Town produced a stunning comeback as goals from Dayle Southwell and Matty Kosylo took their clash with Solihull Moors to a replay.
The Shaymen looked down and out when Adi Yussuf and Nathan Blissett had put Solihull 2-0 up just before the hour-mark.
But the introduction of Cameron King, who set-up Town’s first goal, helped to turn the tie, with Kosylo producing a wonderful free-kick to deservedly rescue a draw.
The sides will meet again at Solihull on Tuesday night.
National League South side Hemel Hempstead Town made it through to the next round by winning 4-2 at Vauxhall Road against Bostik League Premier outfit Wingate & Finchley.
The Tudors were coasting to victory, leading 4-0 with goals from Darren Ward after 19 minutes and 45 minutes and a Sanchez Watt brace in the 33rd and 51st minutes.
But the North London side made the hosts sweat when pulling two back through Sean Cronin in the 55th and 57th minutes – the second from the spot.
National League North fancies Stockport County sailed through to Monday`s draw by hammering National League South side Truro City 5-0 at Edgeley Park.
Truro`s 650-mile round trip was spoiled by a four-goal burst from Matty Warburton in the 3rd, 17th, 27th and 65th minutes, with Darren Stephenson sandwiching the other on the half-hour mark.
A side who do face a long midweek trek for a replay are Evo-Stik Northern Premier League Division One West outfit Ramsbottom United, who shared a 2-2 draw at the Harry Williams Riverside Stadium with Southern League Premier Division South side Weymouth.
Goals from Jake McCarthy after 37 minutes and Calvin Brooks on 83 minutes twice gave Weymouth the lead, with Nic Evangelinos equalising in the 68th minute.
But Iyrwah Godden equalised for the Rams in the 5th minute of time added on at the end of the game, meaning they face a 500-mile round trip to the Dorset coast on Tuesday night.
Steve Claridge`s Wembley dreams are over for another year as his Southern Premier Division South Salisbury side were comfortable beaten 4-1 at Colston Avenue by Bostik Premier hosts Carshalton Athletic.
And that after taking an early 4th minute lead through Aaron Dawson.
Tommy Bradford equalised in the 18th minute, Michael Dixon put the Robins in front after 37 minutes and an Elliot Wheeler own goal made it 3-1 at the break.
Carshalton wrapped up victory with a 76th minute penalty from Paris