Two Danny Lloyd dead-ball strikes in the final seven minutes at Edgeley Park helped the Hatters edge out Marine and ensure a place in the FA Trophy second round.
County have been drawn at home against either AFC Fylde or Brackley Town – who replay on Tuesday night- in the second round.
Leading scorer Lloyd converted a free-kick and a penalty in rapid succession, after the Mariners – who were reduced to ten men for the last half-hour following a straight red card for former Hyde defender Josh Brizell – had taken an early lead, and then regained the advantage on the stroke of half-time in quick response to Kay Odejayi’s equaliser.
County’s line-up included two changes from that which had taken to the field at Cheltenham’s Whaddon Road ground against Gloucester seven days earlier.
John Marsden and the goalscorer on that occasion, Kaine Felix, replaced Jimmy Ball and Mark Ross – with Michael Clarke donning the captain’s armband in the absence of the latter.
Just as the Gloucester match had done, the latest contest saw an early penalty awarded to the opposition – rather spookily, after seven minutes again, although in this instance following Gary Stopforth’s foul on William Smart.
But County keeper Ben Hinchcliffe was unable to repeat his spot-kick saving heroics of a week previously, as visiting captain Danny Mitchley fired Marine ahead.
County went close through John Marsden, whose snap-shot from close range was kept out by the Mariners’ goalkeeper Calvin Hare.
But the Hatters managed to get back on level terms three minutes before the break, when Odejayi headed home Lloyd’s looping cross from the left.
Marine’s lead was then restored in added time, as the visitors broke and Mitchley kept his composure to win a one-on-one duel with Hinchliffe before slotting home.
The Hatters strove to restore parity after the break – with both Sam Minihan and Lloyd firing early efforts narrowly over.
On the hour, Marine’s task of defending the lead was made harder when Brizell received his marching orders for a challenge from behind on Marsden.
Hare played his part between the sticks, as he kept out a goal-bound header from substitute Josh Amis and Lloyd’s low drive.
But it was another defender’s aberration, courtesy of Denzel Williams who handled just outside the area, that led to the award of a free kick after 85 minutes – which Lloyd fired in to the left of Hare for his 12th goal in all competitions.
Lloyd did not have to wait long for his 13th – after going to ground in the box under Lewis Field’s challenge and putting away the penalty to settle a pulsating tie with three minutes of normal time remaining.
FULL-TIME: County 3 (Odejayi, 42; Lloyd, 85 and 87 (pen)), Marine 2 (Mitchley, 7 (penalty) and 45 +1).
County: Hinchliffe, Minihan, Duxbury, Montrose, Clarke (Capt.), Smalley, Felix (Ball, 71), Stopforth, Odejayi (Amis, 71), Marsden (Meppen-Walters, 90), Lloyd. Unused Subs: Ross, Ormson.
Booked: Montrose, Ball.
Man of the Match: Lloyd.
Attendance: 1,411 (163 away).