That said, Palace struggled to really impose themselves on their battling visitors.
Before Shaun Derry's first goal for the club on 39 minutes, Palace failed to create much in the way of clear cut chances. Andrew Johnson had a couple of chances in the first 15 minutes, but had the first smothered by Danny Coyne in the Grimsby goal and shot wide with the second.
Grimsby's best chance of the game came for Darren Mansaram on 20 minutes, but his free header from Steve Livingstone's cross was well off target.
Palace made them pay for that miss when Grimsby failed to fully clear Hayden MullinsÂ’ free-kick from their halfway line and Derry's shot from 20 yards took a deflection off Jason Gavin to give Palace the lead.
Alex Kolinko made a good save from Alan Pouton's shot then lost his footing as Livingstone closed in, but jut managed to recover in time.
Palace changed to 4-4-2 on the hour as Grimsby threatened to rally early in the second half.
Aki Riihilahti replaced Tommy Black and the change instantly distracted Grimsby, who again failed to deal with a ball on the edge of their box allowing Dele Adebola to turn and muscle his way through on the left before shooting powerfully across Coyne and in.
That made up for his glaring miss two minutes earlier. Derry's free-kick rebounded off the post on 77 minutes, but 3-0 would have flattered Palace.
Trevor Francis praised his side’s competitiveness and defending and added: “Grimsby are a side we expect to win against but they use that as their motivation.
“It wasn't a great display but it was the right result.” He was also pleased at Derry being Palace’s 12th different scorer this season.
Paul Groves had no complaints about the result, but was disappointed they didn't take the best chance of the first half and he was unhappy at the free-kick that lead to Palace's first goal being moved forward, saying: “Nevertheless we need to bounce back.”