Grimsby stretched their unbeaten run to five matches at Tamworth thanks to second-half goals from Craig Disley and Alex Rodman.
The hosts started the better and almost went ahead early but Richard Peniket headed a cross wide when well placed.
After a disputed corner Scott Neilson fired in a low cross and Disley skilfully steered his shot home.
The Lambs piled on the pressure in search of an equaliser but Rodman ran clear to seal victory for the Mariners.
VIEW FROM THE DRESSING ROOM
Grimsby Town boss Paul Hurst told BBC Radio Humberside:
"Without a doubt, I don't think you can point the finger at anyone thinking that they took the foot off the gas.
"It was a totally different game to last Saturday but you have to win all types of football matches.
"That's perhaps the most pleasing aspect for me, the way that we won today against a team that ask a lot of questions of you.
"We've got some good players and question marks are always there when things are not quite going so well, but generally I think the team is really starting to come together."
Tamworth 01 Belford 19 Capaldi 21 Thomas Booked 06 Richards-Everton 15 Courtney 29 Hildreth 20 Todd Booked (Wright - 68' ) 35 Croasdale 17 Peniket 09 Richards 28 Chadwick Substitutes 10 Byfield 34 Keane 27 Wright 07 Kerry 08 Baker Grimsby Town 13 McKeown 03 Thomas Booked 12 McDonald 05 Pearson 02 Hatton 11 Neilson (Rodman - 77' ) 08 Disley 07 Colbeck 04 Kerr 14 John-Lewis (Cook - 81' ) 17 Hannah (McLaughlin - 87' ) Substitutes 15 Bignot 10 Hearn 09 Cook 26 McLaughlin 23 Rodman
Ref: Lee Swabey