Town created chance after chance, but only found the back of the net once and in the end were made to pay for their wastefulness.
City looked to be heading for a fifth consecutive defeat, but eventually salvaged a point when they scored with a late penalty.
Grimsby started brightly and threatened Lincoln after just seven minutes when Peter Till set up Simon Heslop, but the striker's shot was charged down.
Grimsby cut Lincoln open again in the 13th minute when a defensive mix-up allowed Till to break. The striker's pass set up Nathan Jarman, but his final shot was straight at Lincoln keeper Rob Burch.
Lincoln went close in the 22nd minute when Lenell John-Lewis got above the Grimsby defence to meet a corner from Stefan Oakes, but saw his header strike the top of the bar.
Grimsby were immediately on the counter-attack with Till bursting through, only for Burch to save at his feet.
Burch then made a double save to prevent Till from scoring before Grimsby finally took the lead in the 38th minute.
Danny Boshell got in front of Lincoln defender Janos Kovacs to send a header into the path of Till and the youngster netted with a left-foot shot from inside the box.
Three minutes before half-time Lincoln's defence was in disarray again with Till once more the dangerman. The speedy striker saw his first shot produce a one-handed save from Burch. When the ball came back to Till he was again denied by the Lincoln keeper.
Lincoln, who rarely ventured forward in the opening 45 minutes, almost snatched a goal in first-half stoppage time, but a shot from Lee Frecklington was blocked by the legs of Town keeper Phil Barnes.
Grimsby were unlucky on the hour when Lincoln defender Frank Sinclair headed against his own bar to keep out another effort from Till.
But the game began to change moments later after a pitch invasion by Grimsby fans.
Lincoln defender Aaron Brown saw his powerful 72nd minute shot well saved by Barnes, but within a minute City were level.
Substitute Sam Mullarkey, making his Football League debut, was brought down by Tom Newey after just two minutes on the pitch.
Frecklington fired the resulting spot-kick low into the bottom corner after sending Barnes the wrong way.