The gutsy visitors defended heroically throughout, but were left with ten men when Tom Newey handled a cross in the box with six minutes left.
The Cumbrians' Basque full-back Aranalde stepped up to thump his spot-kick down the middle of the Grimsby net to hand his side a replay.
The Mariners could hardly complain, despite coming agonisingly close to ripping up the form book against League One form side Carlisle.
Grimsby - 22nd in League Two - had threatened to cause a cup shock until Newey's wandering hand intervened.
The visitors almost netted early on when Paul Bolland's close-range shot was tipped on to the roof of the net by Keiren Westwood.
There was little of the quality football from Carlisle which had seen them reach the summit of League One and inflict a first league defeat on Leeds United last week.
Bolland made Carlisle pay for some slack marking after 28 minutes when he latched on to Martin Butler's flick and lashed a fierce angled volley into Westwood's near post from 12 yards.
Danny Graham should have equalised for the Cumbrians seconds later, but despite being just two yards out, he managed to spoon his shot over the bar.
Soon after that Peter Murphy's header was cleared off the Grimsby line, before Joe Garner smashed the rebound over from close range.
Incessant pressure from the Cumbrians forced the Mariners' defence to work overtime and Phil Barnes' goal led a charmed life, with several shots flashing agonisingly wide.
With the home side running out of ideas, substitute Danny Carlton headed narrowly over, before Aranalde stepped up to equalise.
With the home crowd calling for a winner, Carlisle threw everything forward and Garner was unlucky to see his injury-time shot headed off the goal-line, but Town held on to win a replay.