Tulips captain Nathan Stainfield was sent-off on 75 minutes for a second yellow card before he was joined in the dressing room five minutes later by striker James Tricks, shown a straight red for a stray elbow.
Carlton were unable to make their numerical advantage count with Anthony Howell's header against the crossbar the closest the home side came to scoring in those final 10 minutes.
Prior to the dismissals, Spalding had edged a tight encounter with Jack Steggles in the Carlton goal making good saves from Dan Lawlor and Dan Bannister. But it was a game of few chances with both defences on top.
The point sees Carlton remain in 17th spot but they are now eight points clear of the relegation positions with eight matches left to play.
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