Poole, who joined the club from Bury earlier this month, hit the bar early on but didn’t have to wait much longer for his first Salford goal, opening the scoring inside 20 minutes.
Jordan Hulme soon made it two for the visitors, who were held to a 1-1 draw by Whitby on Saturday, before Poole doubled up for a three-goal lead at the break.
The Emirates FA Cup
First Round Qualifying replays
Wednesday 16 September
Winning clubs receive £3,000
The man-of-the-match nestled the ball in the bottom corner for his hat-trick early in the second half, while Elliot Kebbie made it five on 65 minutes.
Salford’s clean sheet came under threat late on when captain Chris Lynch fouled Michael Roberts in the box but Craig Dootson saved David McTiernan’s spot kick.
The Ammies will now welcome Curzon Ashton to Moor Lane in the Second Round Qualifying on Saturday 26 September.
Elsewhere, Ashton United completed a 3-2 victory at Guisborough Town to knock their hosts – two tiers below them in the pyramid – out of the cup.
After Matthew Chadwick and Danny Earl traded goals on the quarter-hour mark, Chris Baguley put Ashton ahead from the penalty spot – only to be sent off shortly before the break.
Martin Pilkington opened up a two-goal cushion with 20 minutes to play and, although Luke Bythway pulled one back for the home side in the final five minutes, they had done enough.
Bradford Town did, however, cause an upset by backing up their 1-1 draw with Hungerford Town on Saturday with a 2-0 triumph in the replay.
The Western League side play their football two steps below Hungerford but that didn’t stop them progressing to the second round qualifying, courtesy of goals from Michael Rimmer and Tyson Pollard.
And Leatherhead’s clash with South Park was postponed due to a waterlogged pitch, with the re-arranged fixture scheduled for next Wednesday.
For all The Emirates FA Cup First Round Qualifying results click here.
