A Jordan Rose header in the fifth minute of stoppage time ensured National League South side Whitehawk will be in the hat for the FA Cup third-round draw.
The Hawks looked to be heading out of the competition at Dagenham, where they had trailed since the fifth minute when 40-year-old striker Jamie Cureton put the Daggers ahead.
However, a fixture against Premier League opposition in the next round remains a possibility for Brighton-based Whitehawk after Rose forced a replay at the death in a 1-1 draw.
Non-league Altrincham were on the wrong end of some late drama, though, as League One outfit Colchester claimed a 3-2 success at home.
Skipper Jake Moult's measured chip from 30 yards caught Jamie Jones out as the U's fell behind and although Callum Harriott levelled, Michael Rankine put Alty ahead once more in the second half.
That strike was cancelled out by Tom Lapslie before Harriott fired home from just inside the box to ensure Colchester's progress.
Both Chesham and Welling suffered heavy defeats against league opposition in the form of Bradford and Carlisle respectively.
The Bantams knocked out Chelsea and Sunderland en route to the quarter-finals last year and were in no mood to suffer a shock themselves as they ran out 4-0 winners thanks to goals from Kyel Reid, James Hanson, Gary Liddle and Devante Cole.
Carlisle went one better by recording a 5-0 triumph over Welling. Charlie Wyke scored a hat-trick on his birthday, while Antony Sweeney and Danny Grainger were also amongst the goals.
The Wings' chances were not helped by Harry Osborne's second-half dismissal, which came with the Cumbrians 2-0 ahead.
National League high-fliers Forest Green were unable to knock out League Two leaders Oxford as Kemar Roofe's strike 14 minutes from time earned the U's a 1-0 victory.
Paul Tisdale's Exeter were the only club to eliminate a side from a higher division as they consigned Port Vale to a 2-0 defeat at St James Park.
Jordan Tillson opened the scoring and Ollie Watkins added a second late on to secure the Grecians' passage to round three for the first time in 11 years.
Cambridge were on course to dump out Doncaster after leading through Luke Berry, but three second-half goals in the space of 12 minutes - two from Conor Grant and another from Mitchell Lund, earned Darren Ferguson's men a 3-1 win.
David Flitcroft got one over friend Keith Hill as Bury beat Rochdale 1-0 in a derby at Spotland, with Danny Rose, who played under the Dale boss at Barnsley, scoring the early winner.
Finally Graham Westley's Peterborough punched their third-round ticket with a 2-0 success over Luton thanks to goals from Conor Washington and Marcus Maddison.