The Poppies, who were without Rene Howe due to a groin strain, took an early lead on nine minutes in the second qualifying round tie.
Wilson Carvalho sent in a cross and Spencer Weir-Daley touched the ball to Liam Canavan who produced a low finish.
But Witton came back into the game in the latter stages of the half and levelled just before the break when Robert Hopley was on hand to score from the rebound after a header had struck the post.
It looked like the two sides would be doing it again at Latimer Park on Tuesday night.
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But, in the sixth minute of stoppage-time, Wes Benjamin’s 20-yard strike looped over everyone and settled in the net.
AFC Rushden & Diamonds face a replay at Evo-Stik Northern Premier League Division One South rivals Lincoln United on Tuesday night following a pulsating 3-3 draw in the second qualifying round of the Buildbase FA Trophy at the Dog & Duck.
Lincoln took the lead inside five minutes when Robert Norris’ cross from the right was swept home by Jordan Hempenstall.
But Diamonds reacted well and levelled things up when Lewis Leslie headed home a Nic Evangelinos corner.
However, the visitors regained the lead on 25 minutes when James Blunden’s downward header from a Norris free-kick found the corner.
Diamonds were back on level terms again early in the second half when Jake Newman’s low cross found Taylor Orosz and his effort was deflected in.
But Lincoln took the lead for a third time on 57 minutes when Finlay palmed a Norris strike onto the crossbar and Gary King was left with the simple task of scoring from the rebound.
Diamonds went close when Newman hit the outside of the post after his initial effort was blocked by Jack Turner, who had parried an Evangelinos shot into the frontman’s path.
But a third equaliser did arrive when Sam Brown’s long throw was flicked on and Nabil Shariff beat Turner with a fine header.
And that proved to be the end of the scoring and Diamonds now have a replay to look forward to in midweek.
Corby Town’s problems continue to mount as they slipped to the foot of the Evo-Stik Northern Premier League Premier Division after they were beaten 1-0 at Workington.
Gary Mills handed league debuts to new signings Jamie Tank, Phil Trainer and Stefan Moore while Robbie Parsons, who joined from AFC Rushden & Diamonds, was named on the bench.
But the Steelmen fell behind on 17 minutes when Gari Rowntree’s ball over the top sent Scott Allison in on goal and he chipped the ball over the onrushing Aidan Grant.
That proved to be the winner as, despite performing better in the second half, Corby were unable to find an equaliser.