Chris Kinnear and his Dover side put their name in the hat for the next round with a 1-0 win at home to Morecambe.
Stefan Payne's strike on the stroke of half-time was enough to put the Conference strugglers through at the expense of Jim Bentley's men.
Roots Hall was left stunned as Southend United, seventh in League Two, were eliminated at home by Chester.
Goals from Ben Heneghan and Craig Mahon, either side of a Barry Corr penalty, sent the visitors through to the next round.
Another shock came as League Two Cheltenham Town thrashed 10-man Swindon Town, who sit third in League One, 5-0.
A hat-trick from Byron Harrison, along with goals from Matt Richards and Terry Gornell, made for a special afternoon at Whaddon Road on a day that Swindon's Nathan Thompson will want to forget after his early dismissal.
Bury survived an early scare against Isthmian League side Hemel Hempstead as they came from a goal down to win 3-1, while Conference leaders Barnet were beaten 3-1 at home by Wycombe Wanderers despite taking the lead through John Akinde.
Port Vale and MK Dons were involved in a seven-goal thriller, which the latter won 4-3.
Fellow League One sides Barnsley, Bristol City, Oldham Athletic, Peterborough United and Yeovil Town were able to progress on Saturday, together with League Two outfits Cambridge United, Oxford United, Hartlepool United, Luton Town, Plymouth Argyle and Tranmere Rovers.
Conference Premier sides Eastleigh and Dartford also made it to the second round, coming through against fellow non-league teams in the form of Lincoln City and Bromley respectively.
Mansfield Town's clash with Concord Rangers was abandoned, along with the tie between Weston Super Mare and Doncaster Rovers.
There will be replays in a number of ties, with Sheffield United, who were held by Crewe Alexandra, among those to draw.
