Eastleigh next up as Dragons finish in fourth place.
This proved not to be a play-off dress rehearsal in the end after Jason Oswell and Nicky Deverdics both stuck to ensure the win, while AFC Fylde went down to a defeat at home to FC Halifax Town.
The Dragons will now entertain Eastleigh in the play-off qualifying round on Thursday, with the winners advancing to a semi-final at Salford City the following Sunday.
It was a slow start to proceedings from both sides, not helped by the conditions, but it was the visitors who struck first, a corner from Joe Leesley was not dealt with by the Dragons defence, the ball falling to Mark Beck to hold off Kevin Roberts and smash into the top corner.
The closest Wrexham came to troubling Joe Cracknell in the opening stages came as Rutherford saw a shot deflect wide for a corner, from which Jason Oswell was unable to generate any power as his effort cannoned off a defender, and Spyrou guided a tame header into the hands of the Town keeper as he reached James Jennings' cross.
Kevin Roberts sliced a Jack Muldoon cross away for a corner while Muldoon fired straight at Dibble as the half wore on, the Town attacker allowed far too much space from which to advance from deep.
But Wrexham were back on level terms two minutes later in an exciting end to the half.
Oswell registered his first Wrexham goal as he headed beyond Cracknell from Rutherford's cross, before Beck saw a header at the other end crash off the top of Dibble's bar.
And then in added on time Agustien needlessly gave away a clear penalty, his pull on Muldoon not going unnoticed by the officials, Dibble guessing the right way to push clear the ensuing spot kick from Muldoon.
Harrogate again started the brighter after the interval and only a last ditch block from Roberts denied Muldoon a sight of goal as the Dragons failed to clear their lines, while Dibble did well to get down and save at the near post from George Thomson after the visitors broke quickly from the back.
An unmarked Muldoon dragged a first time volley wide of the mark after finding space in the Dragons box to meet Aaron Williams' cross.
A flicked Oswell header gave Cracknell a nervy moment, the Town keeper spilling the effort but only at the expense of a corner before a Spyrou header was deflected wide soon after, each effort coming either side of a curling Leesley shot that had Dibble scrambling across goal.
Carrington needed to be alert to intercept a Beck effort after a mix up between Jennings and Deverdics gave Williams the chance to cross, Cracknell comfortably holding an Agustien effort at the other end soon after.
Leesley was not far away with a powerful drive after Agustien was beaten to a 50-50 ball by Beck, Jennings not quite a close with an effort at the other end from a free kick, his shot starting off target and drifting further away from goal.
And for all the pressure the Dragons had been forced to withstand they went ahead 10 minutes from the end, Rutherford sending Carrington clear on the right, his cross met perfectly by half time replacement Nicky Deverdics to slot home first time.
Muldoon, who was denied a chance moments earlier by standing water on the pitch, headed straight into the hands of Dibble as he met Williams' cross, before Wrexham were able to see out the game and set up a play-off clash with the Spitfires.