Robert Briggs put the Mariners in front from the penalty spot after 12 minutes.
Gainsborough fought back through George Hornshaw's strike just minutes after the second-half restart to give the hosts a share of the spoils, extending their unbeaten run to three games.
Meanwhile, Whitby Town climbed up to 14th place with a 2-1 victory at home against Marske United.
Goals from Harry Green and debutant Shaun Tuton gave the Seasiders their 10th win of the season.
A clash between two play-off hopefuls at the Proctor Cars Stadium saw Guiseley take all three points in a 1-0 victory over Matlock Town.
Jameel Ible's third-minute goal takes the Lions just three points away from a play-off spot.
In the evening's final fixture, Ashton United fought back to earn a point on the road at Stafford Rangers, after Nathan Lowe's emphatic finish cancelled out Tom Tonks' first half penalty.
Results - Tuesday 15 Feburary
Gainsborough Trinity 1-1 South Shields
Matlock Town 0-1 Guiseley
Stafford Rangers 1-1 Ashton United
Whitby Town 2-1 Marske United
Photo credit: Kev Wilson Photography
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