The League Two side dominated their National League South opponents for almost the entirety of the contest, but had to wait until the 76th minute to break the Beach Boys' resistance.
Without a competitive fixture in almost three months following the abandonment of non-league football below the fifth tier, the Essex outfit dug deep to frustrate Simon Weaver's men, only to eventually succumb to Josh Falkingham's late goal.
And although losing in such fashion will be tough for a valiant Rangers team to swallow, they could easily have found themselves behind much earlier were it not for an inspired goalkeeping display by man of the match Chris Haigh.
Town wasted little time getting going, taking a fourth-minute left-wing corner short for George Thomson to cut inside and force Haigh into a decent save at his near post.
The Sulphurites continued to dominate possession, though there was a moment of concern at the other end when Lamar Reynolds ran onto a ball over the top, checked back and eventually saw an effort blocked by Connor Hall.
Jon Stead then spun inside the Rangers box and bent a left-footed strike narrowly wide of the far post, before missing a glorious chance to break the deadlock on 25 minutes as he shot tamely at Haigh from close range having got on the end of Dan Jones' low centre from the left.
And it was the men in all black who continued to look the more likely, Lloyd Kerry stinging the palms of Haigh from distance just moments after Will Smith was fortunate to escape conceding a penalty having put two hands in the back of Reynolds.
Town went closer still seven minutes before the interval as Stead drove down the left and unleashed a shot that was deflected goalwards by Tyrone Sterling, however the wrong-footed Haigh showed fine reactions to somehow divert the ball over the cross-bar with his leg.
Half-time arrived with Harrogate having been very much the better team and in almost complete control, but without really looking anywhere near their best.
And the second period began in similar fashion as Weaver's troops continued to boss proceedings while lacking the required ruthlessness in and around the Concord penalty area.
Josh McPake and Jones both saw decent strikes blocked shortly after the resumption, however Town might have found themselves behind after 55 minutes.
Having failed to deal with a long throw-in from the left, the ball was nodded into the path of an unmarked Jack Cawley by Ryan Charles, though the big defender somehow cleared the bar when it looked easier to score from no more than three yards out.
A brief spell where the Beach Boys just started to look a little bit more threatening safely negotiated, Town reclaimed the ascendancy after introducing Mark Beck and Ryan Fallowfield from the substitutes' bench.
Only a fine last-ditch challenge prevented Beck from converting Falkingham's cross from the right at the near post, then Haigh did well to turn a Thomson volley around his post.
The recently arrived Brendan Kiernan was next to go close, nodding a difficult chance wide of the mark from Kerry's lofted pass, but a breakthrough finally arrived on 76 minutes following a probing run infield off the left by Jack Muldoon.
Town's leading marksman stroked the ball beyond the despairing dive of Haigh from just outside the box, and although his effort rebounded off the foot of the upright, Falkingham followed up to side-foot into a gaping net.
Concord did their best to mount a late response, but it was at the opposite end of the field where a second goal of the day looked more likely to materialise, Haigh again coming to his side's rescue with stops to deny Beck and then Muldoon at the death.
Concord Rangers: Haigh; Pollock, Roast (Martin Sorondo 83), Sterling, Cawley, Payne; Blanchfield (Wall 79), Blackman, Simper; Reynolds, Charles (Babalola 59). Unused substitutes: Wilks, McFadden, Search, Hernandez.
Harrogate Town: Cracknell; Burrell, Smith, Hall, Jones (Fallowfield 62); Thomson, Falkingham, Kerry, McPake (Kiernan 67); Muldoon, Stead (Beck 61). Unused substitutes: Belshaw, Francis, Lokko, Williams.
Referee: P Bankes (Lancashire).