Crewe, who lost 3-0 at home on Saturday, made four changes for their trip to Blundell Park and were the better side from start to finish. With steadier finishing they could have had more than three goals but the victory sent their supporters home happy.
Crewe almost scored from their first corner on five minutes when a David Vaughan shot was blocked on the line but the breakthrough came on 38 minutes. Luke Varney played through his strike partner Nicky Maynard and he coolly finished from 12 yards.
Despite controlling play Crewe failed to score again until the 73rd minute but it was well worth the wait. Varney once again did the spade work and his left-wing cross was brilliantly converted with a first-time 20-yard effort from 18-year-old Michael O'Connor.
And the icing on the cake was supplied in the final minute when Maynard was brought down in the box by Tom Newey and Ryan Lowe easily converted to make it 3-0.
Although the Crewe keeper Stuart Tomlinson, who was brought in for Ben Williams, had little to do he made a good save in each half to ensure that Alex kept a clean sheet.
After their poor start in the league following relegation this was a timely tonic for Crewe but they will face a stiffer task at Brighton on Saturday.
For Grimsby's new management team things are starting to look ominous though and they clearly need new blood throughout the team to mount a serious promotion challenge.