Oldham Athletic created the biggest upset when they knocked out League One leaders Wolverhampton Wanderers 2-1 at Molineux.
Goals in either half from Danny Philliskirk and Adam Rooney were enough for the Latics to progress, despite a stoppage-time goal from Leigh Griffiths.
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Boreham Wood look set to pull off their own cup shock when Luke Garrard put them ahead from the spot away to Carlisle United.
Garrard had another opportunity from 12 yards moments later, but saw his penalty saved by Greg Fleming.
Lee Miller pulled the Cumbrians back into the game 10 minutes from the end, before Mark Beck completed the comeback with a heartbreaking injury time winner, which sees United earn a home tie against Brentford.
Clayton McDonald's second-half header helped Grimsby win away at Scunthorpe and secure the Conference, which earns them a home tie against Northampton Town.
Robbie Wilmott's goal on the stroke of half time was enough for Newport County to edge past Braintree Town.
The South Wales outfit will travel to Kidderminster in round two.
Wycombe Wanderers eased past League Two Crewe Alexandra at Gresty Road thanks to a Steven Craig penalty and Gary Doherty's 70th-minute winner.
Bristol Rovers were on course for a convincing win away to York City when goals from John-Joe O'Toole, Oliver Norburn and Chris Beardsley put the Gasheads into a three-goal lead.
However, Wes Fletcher brace in as many second-half minutes gave City hope, but Rovers were able to hold on and book a place in round two, where they host Crawley Town.
Non-league Cambridge United have earned a replay after holding League Two Bury to a goalless draw at Gigg Lane.
The game was rescheduled after their original fixture was rained off.
Results in full: Bury 0-0 Cambridge, Carlisle 2-1 Boreham Wood, Crewe 0-2 Wycombe, Newport County 1-0 Braintree Town, Scunthorpe 1-2 Grimsby, Wolves 1-2 Oldham, York City 2-3 Bristol Rovers
