Boro named an unchanged side from their 3-1 win against North Ferriby on Tuesday night, and could've gone ahead after eight minutes, but James Walshaw's header was well saved by Martin Fearon in the Marine goal.
Tommy Taylor had to be alert to keep out Marine skipper Danny Mitchley's effort away and then at the other end, James Cadman's effort just arrowed wide of the post.
Boro almost went ahead again on 24 minutes, Michael Coulson skipping around Fearon, but his resulting effort on goal was hacked off the line and away to safety.
Again, Steve Kittrick's side ploughed forward in search of the opener, but Walshaw, Waybe Brooksby and Leon Scott were all denied.
Taylor was again tested on 39 minutes, as he had to superbly tip Chris Doyle's header onto the bar and Josh Lacey cleared the danger and the sides went in level at the break.
Marine led after 55 minutes, Josh Hine scoring on the rebound after James Short's shot was palmed out by Taylor.
But back battled Boro, Walshaw heading home from close-range to level matters up.
The referee then took centre-stage, sending centre-back Kev Burgess for an early bath on the hour mark with a straight red card.
The 10 men of Boro battled on and had the best chance to nick the win and seal a spot in Monday's draw, but Walshaw's headed effort was superbly kept out by Fearon and the game ended all-square.
The two sides will meet at the Flamingo Land Stadium on Tuesday night to see who moves into the next round of the competition.
DON'T MISS: Full round up of Boro's FA Cup excursion in Thursday's Scarborough News.
WATCH: Boss Steve Kittrick's post match reaction here: https://www.thescarboroughnews.co.uk/sport/football/boro-video-boss-kittrick-reacts-to-fa-cup-draw-at-marine-1-9340476