Chris Clements' opener was cancelled out by Isaac Vassell before, with the game into five added minutes, referee Mark Haywood pointed to the spot after Danny Collins handled in the box.
But after his dramatic return to the side following Dean Henderson's recall to Manchester United, Grimsby's long-serving keeper kept out Danny Hylton's spot-kick to preserve a share of the spoils.
After a tight, goalless first half, Luton re-started brightly, with Brandon Comley having to hack clear a low cross from on the line.
But just as the visitors were starting to step up a gear, Grimsby broke the deadlock when Ben Davies - after seeing an effort charged down - kept the move alive with a fine, hanging cross to the far post, where Clements powered his header home from close range.
However, the Hatters hit back when Pelly Ruddock nipped in at the corner and crossed into the area, where Vassell headed home despite McKeown's best efforts.
They looked to have sealed the victory when they were awarded their 95th-minute penalty, but McKeown was to prove Grimsby's saviour.
Report supplied by the Press Association
Match ends, Grimsby Town 1, Luton Town 1.
Second Half ends, Grimsby Town 1, Luton Town 1.
Brandon Comley (Grimsby Town) is shown the yellow card for a bad foul.
(Grimsby Town) wins a free kick in the defensive half.
Foul by Danny Hylton (Luton Town).
Penalty conceded by Brandon Comley (Grimsby Town) with a hand ball in the penalty area.
Penalty saved! Danny Hylton (Luton Town) fails to capitalise on this great opportunity,  right footed shot saved  in the top centre of the goal.
Foul by Ben Davies (Grimsby Town).
Jack Senior (Luton Town) wins a free kick on the left wing.
Sam Jones (Grimsby Town) wins a free kick in the attacking half.
Foul by Jack Marriott (Luton Town).
Shaun Pearson (Grimsby Town) wins a free kick in the defensive half.
Foul by Danny Hylton (Luton Town).
Corner,  Luton Town. Conceded by Danny Andrew.
Corner,  Luton Town. Conceded by Danny Collins.
Corner,  Luton Town. Conceded by Ben Davies.
Substitution, Luton Town. Jack Marriott replaces Isaac Vassell.
Attempt saved. Jordan Cook (Luton Town) right footed shot from the centre of the box is saved in the top centre of the goal.
Foul by Sam Jones (Grimsby Town).
Alan Sheehan (Luton Town) wins a free kick in the attacking half.
Substitution, Grimsby Town. Scott Vernon replaces Callum Dyson.
Substitution, Grimsby Town. Akwasi Asante replaces Adi Yussuf.
Substitution, Grimsby Town. Sam Jones replaces Chris Clements.
Attempt missed. Jordan Cook (Luton Town) right footed shot from the centre of the box is too high.
Foul by Adi Yussuf (Grimsby Town).
Scott Cuthbert (Luton Town) wins a free kick in the attacking half.
Foul by Adi Yussuf (Grimsby Town).
Alan Sheehan (Luton Town) wins a free kick in the attacking half.
Foul by Adi Yussuf (Grimsby Town).
Alan Sheehan (Luton Town) wins a free kick in the attacking half.
Ben Davies (Grimsby Town) wins a free kick in the defensive half.
Foul by Pelly Ruddock (Luton Town).
Goal!  Grimsby Town 1, Luton Town 1. Isaac Vassell (Luton Town) header from the right side of the six yard box to the high centre of the goal. Assisted by Pelly Ruddock.
Jack Senior (Luton Town) is shown the yellow card for a bad foul.
Ben Davies (Grimsby Town) wins a free kick on the left wing.
Foul by Jack Senior (Luton Town).
Attempt saved. Callum Dyson (Grimsby Town) right footed shot from outside the box is saved in the centre of the goal.
Ben Davies (Grimsby Town) wins a free kick in the attacking half.
Foul by Ollie Palmer (Luton Town).
Corner,  Grimsby Town. Conceded by Jack Senior.
James McKeown saved a stoppage-time penalty to earn Grimsby a point against Luton.