The Mariners never really looked in danger against opposition from two levels lower in the non-league pyramid, although they had to wait until after the half-hour before taking the lead through a Ross Hannah penalty.
Rushall gave a good account of themselves and created several half-chances but Town’s progress was secured when Shaun Pearson made it 2-0, before Andy Cook added a third.
Grimsby boss Paul Hurst made his cup intentions clear by naming a strong line-up for the visit of the Pics.
Just two changes were made to the starting XI from the team that beat Forest Green Rovers last week, with Clayton McDonald replacing Chris Doig and Scott Neilson coming in for Joe Colbeck.
James McKeown started in goal, with Sam Hatton, Pearson, McDonald and Aswad Thomas making up the back four.
Alex Rodman, Craig Disley, Scott Kerr and Neilson were the midfielders, with Cook and Hannah again paired in attack.
FA Cup rules allow seven substitutes, so reserve goalkeeper Jonathan Hedge, Colbeck, Liam Hearn, Paul Bignot, Andi Thanoj, Richie Jones and Patrick McLaughlin were all named on the Grimsby bench.
Rushall made the trip from the West Midlands looking to cause their second successive shock after knocking out Skrill North Stockport County in the previous round.
The Evo-Stik Premier division outfit named veteran striker Dele Adebola in their starting line-up, while Liam Spink scored a hat-trick in last week’s FA Trophy win over Barwell.
Town had the first shooting chance when the ball fell for Disley on the edge of the box but his effort went wide.
Rushall were also looking to attack in the early stages and winger Carl Palmer sent a low cross over from the right that McKeown had to dive to stop.
The hosts won the first corner on seven minutes but McDonald could not get on the end of Kerr’s delivery at the far post.
The big central defender was penalised for a foul on Ahmed Obeng five minutes later to give the visitors a free kick on the edge of the Town box but full-back Jimmy Turner wasted the opportunity, blasting his shot over the bar.
Another Rushall free kick, this time taken by Mitchell Tolly, also caused no problem for McKeown as the shot went straight at him.
Cook did well to rescue a Thomas cross at the far post as the 20-minute mark approached but he could not pick a team-mate out.
A penalty appeal from the visitors came when Tolly went down under a challenge inside the Mariners box but the referee was not interested in the claims, signalling instead for a goal kick.
Neilson won a corner on the left as Town continued to attack in search of an opening goal and from it, Hannah forced a good save out of visiting keeper Chris Gemmell with a shot from 15 yards.
A foul on Cook in the air gave Grimsby a free kick inside the Rushall half on the half-hour and McDonald elected to shoot from it but his 35-yard effort flew over the bar.
Town were given a golden opportunity to open the scoring two minutes later when Neilson was brought down inside the box and the referee gave a penalty. HANNAH converted the chance, smashing the ball into the keeper’s bottom-left corner.
The home side were on top now and Thomas sent another cross over after a run down the left but it proved just too long for Cook, who could only head back to keeper Gemmell.
Obeng had been Rushall’s most dangerous player so far and he won a free kick 25 yards out after a tricky run through the middle on 40 minutes. From it, Spink cleared the bar with his shot.
Kerr was booked for a foul just inside the Rushall half as the game moved towards stoppage time and from the resulting free kick, Adebola almost worked enough space to get a shot away but Thomas eventually cleared.
One added minute was played and with no further chances, the Mariners took a narrow lead into the dressing rooms with them at the interval.
No changes were made before the restart and Town had the first chance of the second half when Neilson hit a low shot that Gemmell had to push away for a corner.
At the other end, Kristian Ramsey-Dickson dragged a low attempt just wide of McKeown’s far post from the edge of the box.
A foul on Palmer gave Rushall a free kick on the edge of the Town penalty area and after the initial shot was blocked, the ball was worked to Ramsey-Dickson, who sent his header off-target.
Luke Bottomer replaced Spink for the visitors on the hour, before Town had a chance to double their lead when Cook found Neilson on the left. The winger advanced to the edge of the box and picked out Hannah but he could only fire wide.
Hearn came on for Hannah as Grimsby made their first substitution on 65 minutes and another chance came when Cook connected with a cross from Hatton but his header dropped wide of Gemmell’s goal.
Thomas won a corner on the left two minutes later but Pearson was beaten to Kerr’s ball by Tolly, who cleared for another corner. This time, Gemmell came off his line to claim the catch.
Stan Mugisha was the next Rushall sub to come on as he replaced Obeng with 20 minutes to go, before Town introduced Colbeck for Rodman soon afterwards.
Right-back Turner was booked for a foul on Thomas which gave Grimsby a free kick midway inside the Pics half. From it, the Mariners made the game safe when Kerr’s delivery was headed into the net by PEARSON.
And any remaining doubt was ended when COOK raced through on 79 minutes and finished well, sliding the ball past Gemmell for 3-0.
Tom Eckersley replaced Adebola for Rushall after Jones was sent on in place of Kerr as both sides used up their substitutions.
Hearn had a chance to make it four for the Mariners with six minutes to go but he could only hit the side netting at the near post from a tight angle.
Turner escaped a second booking for a foul on Neilson as the game moved into three minutes of stoppage time and Hearn had a late opportunity to get on the score sheet but hit his effort straight at Gemmell from inside the box.
Town return to league action away to Woking on Saturday.
The FA Cup With Budweiser First Round Proper Draw will take place tomorrow at 1.30pm – live on ITV.
Catch the highlights of today's game on Mariners Player soon.