The two sides were level after 90 minutes of their Third Round Qualifying replay and it was not until the fifth minute of extra-time that Ramone Rose put Staines in front.
It looked as though that would be enough to give the visitors the victory, but a last-minute equaliser from striker Jack Maloney sent the game to penalties.
The FA Trophy
Third Round Qualifying
Tuesday 2 December 2014
Winners receive £4000 from prize fund
By Simon Collings
From there, the tie went to sudden-death and after Staines missed, it was left to goalkeeper Nick Hutchings to fire Poole into the next round.
There was extra-time elsewhere in Tuesday’s FA Trophy replays, with both Bath City and Weston Super Mare progressing as a result.
Bath toppled Gloucester City 3-1, while Weston Super Mare saw off Bedford Town 3-2 after the teams had been level at 1-1 following 90 minutes of play.
The remaining five ties proved to be tight affairs, with just 13 goals scored in the replays.
Two sides claimed away victories, with both Chorley FC and Guiseley AFC picking up wins against Stalybridge Celtic and Rushall Olympic respectively.
Chorley booked their spot in the next round thanks to goals in either half from Jack Lynch and James Dean, while Guiseley fought back from 1-0 down courtesy of strikes from Jake Lawlor and Gavin Rothery.
Elsewhere, there were home wins for Didcot Town, Bromley and AFC Sudbury.
Didcot’s replay victory came against Merthyr Town, with the home side crawling their way back from a goal down to claim a 2-1 win.
It was tight affair for Sudbury too, who overcame St Neots Town 1-0 thanks to a brilliant 30-yard strike from Lawrence Yiga at the start of the second-half.
On the other hand, Bromley enjoyed a more comfortable night’s work, booking their spot in the First Round with a 3-0 win over Tonbridge Angels.