After a goalless first half, Djabi put Fleetwood in control from the penalty spot after Jordan Hancox was fouled in the area.
And Djabi was not done there - Hartlepool captain Jack Turnbull was shown a red card after bringing him down when the Fleetwood man was through on goal, and he headed in his second 20 minutes from full-time to clinch a 2-0 victory.
The FA Youth Cup
First Round Proper
Tuesday 3 November
Cheltenham Town were big winners in their local derby with Swindon, Lewis Thompson scoring a second-half double in a 5-1 victory.
Tom Smith levelled up for Swindon after Karnell Chambers had opened the scoring, though Matthew Bower restored Cheltenham’s lead just before the break.
Cheltenham did not look back from there as Thompson, who had a number of chances in the first half, scored either side of an Alex Dinsmore strike.
Ebbsfleet United recovered from a goal down to emerge triumphant in dramatic fashion from Gillingham.
Darren Oldaker’s sublime free-kick put the Gills ahead early on but Harry Stannard’s sending off midway through the first-half made it an uphill struggle from there on in.
Gillingham held out until the 67th minute and a Karn Miller-Neave penalty, before Caleb Bearman-Dyce grabbed the all-important goal for Ebbsfleet seven minutes before time.
Morecambe were made to work hard for a 2-1 victory over North Ferriby United as Morgan Homson-Smith scored his second goal and the winner with the last kick of the game.
And Jack Dyche and Noel Burdett were the inspiration behind a Scunthorpe victory by the same scoreline against ten-man Wrexham.
Jack Fixter drilled the ball home from the edge of the area in the sixth minute for Lincoln City, who kept things tight at the other end to come away with a 1-0 victory against Port Vale.
Sholing also suffered spot-kick agony on the night as after a goalless draw, Newport County progressing to the next round by 4-2 on penalties.
Elsewhere six different goalscorers scored for Southend United in their 6-1 triumph over Barton Rovers, Oxford United also racked up six goals against Kidlington and Leyton Orient took away a 2-0 win from Hornchurch.
