His strike, coming after some excellent work from Jack Muldoon, was no more than Simon Weaver's side deserved, although they were made to fight every step of the way.
The 1-0 win saw Town lift the trophy for the first time in their history and came almost nine months to the day since their previous visit to Wembley culminated in promotion to the EFL.
Simon Weaver's side was expected, despite a number of players having pressed their claim for a place in the starting line-up in Friday's 5-4 win against Cambridge.
Rangers, who needed replays, extra-time and penalty shoot-out wins to advance to the final of the competition were playing their first competitive fixture since a 1-1 draw at Eastbourne Borough back in mid-February before their league season was curtailed.
Weaver saw his Town side make the early running with Will Smith testing keeper Chris Haigh in the first couple of minutes from a Dan Jones long throw.
Haigh then parried away the danger from George Thomson's effort before reacting sharply to cut out the danger from a Lloyd Kerry cross.
After weathering the early spell of pressure Rangers began to find their feet. A long ball set Ryan Charles free but Connor Hall used his strength well to regain possession.
Another direct passage of play freed the dangerous Lamar Reynolds before the Town defence crowded him out and recovered the danger.
On 17 minutes Jon Stead received a pass on the edge of the box from Warren Burrell and his smart turn and shot was not far wide of Haigh's right-hand post.
The forward, playing in his 699th career game then had a headed effort that landed just over the bar as Town begin to settle into their stride.
The Beach boys were managing to hold Town at bay though and on 25 minutes they had their first meaningful effort on goal courtesy of a long range effort from midfielder Sam Blackman.
Minutes later Thomson pounced on a defensive error and Rangers were indebted to Jack Cawley who cleared the danger on the line.
Jack Muldoon then had an effort scrambled clear as Town looked to press territorial advantage.
Lloyd Kerry, finding himself with space in front of him, drove forward to hit a sot from distance but once again Haigh was equal to the task.
Stead then had Town's best chance of the first-half when his mazy run saw him get a left-footed strike away that took a deflection of captain Tyrone Sterling forcing Haigh to make a late adjustment to tip the ball away to safety.
On the stroke of the half Town's Dan Jones went into referee Bankes' book when he pulled back Reynolds.
Town began the second half with an increased urgency to their play, pressing the Rangers defence back in and around their 18-yard box and from a Thomson corner Jones's volley took a deflection just wide of the goal.
Town had a huge scare on 55 minutes though when Concord's hopes of an upset almost came to fruition when a loose ball fell perfectly to Cawley inside the six-yard box but his attempt went over the bar with the goal at his mercy.
On the hour mark Waver responded by making a double-change. Off went Jones and Stead to be replaced by Ryan Fallowfield and Mark Beck.
Fallowfield was immediately into action, with his pace and energy causing problems and from one of his forays forward a Beck near post effort went narrowly over.
Haigh then saved smartly from Thomson before a third change for Town saw Brendan Kiernan introduced for McPake.
Haigh was again in the thick of the action as he clashed with Beck as the Town substitute bore down on goal as the game entered its final quarter.
Kiernan then headed wide when placed and Beck headed over but with opposition legs tiring Town finally struck.
Muldoon's penetrating run from the left saw him cut inside his man before unleashing a shot that rebounded off the post, only to be met by the onrushing Falkingham to crash home.
It was no more than Weaver's side deserved having racked up over 20 efforts on goal and immediately after falling behind Rangers made a further change when they brought on top scorer Alex Wall.
Having got the lead Town were in no mood to relinquish the lead and both Beck and Muldoon almost doubled the leadf before the full-time whistle sparked jubilant celebrations.
Harrogate Town: Cracknell, Burrell, Jones (Fallowfield, 61), Smith, Hall, Thomson, Falkingham, Kerry, McPake (Kiernan, 67), Stead (Beck, 61), Muldoon.
Subs not used: Belshaw, Lokko, Francis, Williams.
Goals: Falkingham (76).
Booked: Jones (44).
Concord Rangers: Haigh, Payne, Roast (Martin, 83), Pollock, Cawley, Blanchfield (Wall, 79), Blackman, Simper, Charles (Babalola, 59), Sterling, Reynolds.
Subs not used: McFadden, Wilks, Search, Hernandez.
Referee: Peter Bankes.