The Iron controlled possession against their rivals, but goals form Louie Soares and ensured it was the Mariners who go through to face Lincoln in the final.
Bobby Grant flicked two early headed efforts wide, but the visitors had the best early chance when Sam Hatton hit the crossbar - via Sam Slocombe's fingertips - from a free-kick and Greg Pearson's effort from the rebound was also turned away by the home keeper.
Anthony Elding put the ball in the back of the net, but he was in an offside position so it was chalked off.
Grimsby took the lead after 39 minutes when Soares' shot was turned past Slocombe.
The second-half started slowly, with Mark Duffy bringing the first safe from cc McKeown on the hour mark.
Connor Jennings and Ronnie Gibbons came on for Grant and Andy Barcham as the Iron chased the game, but an individual effort from Andy Cook put the away side two goals ahead and effectively killed off the tie.
The home side did not give up, though, with Mike Grella, Christian Ribeiro and Jennings all having chances.