The biggest gulf between first-round sides on Saturday was the 88 places that separated League One outfit Stevenage and visitors Guiseley, who sit four tiers lower in the Northern Premier.
Guiseley’s Will Longbottom levelled with seven minutes left to force extra time and then penalties after Jamie Reid had fired Stevenage in front, but Jameel Ible saw the final spot-kick saved as the hosts edged the shootout 5-4.
The National League, meanwhile, claimed several scalps over EFL opponents.
Dion Pereira’s second-half penalty gave Dagenham and Redbridge victory at Crewe who sit fifth in League Two, while James Norwood and Jesurun Uchegbulam helped Oldham fight back to beat fourth-tier Tranmere.
Wealdstone are in the National League relegation places, but put their league form behind them as Alex Reid’s 90th-minute winner sunk League Two Grimsby.
But a 95th-minute equaliser denied National League strugglers Maidenhead United a place in round two for the first time in 138 years.
Shawn McCoulsky put Alan Devonshire’s side ahead at home to League One strugglers Crawley, who sit 45 places higher in the league ladder, but Toby Mullarkey’s stoppage-time strike sent the tie into extra time.
And Tola Showunmi bagged the winner with four minutes of extra time remaining.
Remaining first-round fixtures
Sunday:
Milton Keynes Dons v AFC Wimbledon (12:30)
Sutton United v Birmingham City (12:30)
Boreham Wood v Leyton Orient (14:00)
Curzon Ashton v Burton Albion (14:00)
Harrogate Town v Wrexham (15:30)
Monday:
Chesham United v Lincoln City (19:15)