Andy Cook's goal just after the hour mark was enough to see Grimsby get their first ever win at the Lamb.
Cook got his second of the season just six minutes after coming on as a substitute as the Mariners remain unbeaten away from home.
Joe Colbeck had two long-range efforts in the first half for Grimsby while Ross Hannah forced a good save out of Tamworth keeper Tony Breedon.
Grimsby are third in the Blue Square Bet Premier, three points off top spot.
VIEWS FROM THE DRESSING ROOM
Grimsby Town joint boss Paul Hurst told BBC Radio Humberside:
"We lost a couple of players last week with bookings and suspensions, but today, we can, we did our job
"It wasn't pretty to watch for large parts of the game but ultimately it's a result.
"We've come away from here with a 1-0 victory against a team who we didn't have a good record against."
Tamworth 06 Marshall 15 Courtney 30 Oji Dismissed 35 Taylor 08 Hendrie (Kelly - 72' ) 11 Kerry 13 Breedon 18 Till (Tait - 73' ) 19 Barrow Booked 07 Cunnington (Moke - 72' ) 09 Wright Substitutes 31 Belford 02 Tait 03 Kelly 34 Moke 28 Collins Grimsby Town 13 McKeown Booked 03 Thomas 06 Miller 04 Niven 07 Colbeck 08 Disley 19 Wood 22 Pond 26 Marshall Booked (Artus - 90' ) 09 Elding (Cook - 57' ) 25 Hannah (Southwell - 86' ) Substitutes 02 Hatton 11 Artus 21 Thanoj 12 Cook 20 Southwell