Grimsby moved to within three points of a play-off place, but were pegged back despite taking the lead at Tamworth.
Home goalkeeper Jonathan Hedge produced two saves to deny Liam Hearn and Shaun Pearson as the Mariners started well.
They took a deserved lead when defender Ian Miller powerfully headed home from Michael Coulson's corner.
Tamworth, who have now failed to win in eight matches, equalised when substitute Connor Taylor finished from close range after Richard Tait's pass.
The point lifts Grimsby up to seventh place in the Blue Square Bet Premier table, three points behind York City in fifth spot.
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Grimsby joint-manager Paul Hurst told BBC Radio Humberside:
"Frustrated again really, we got ourselves in front and thought that would make a big difference against them and open the game right out but we didn't probably hold on to the lead quite long enough.
"After working hard and sort of probing without been at our best to get ourselves in front we concede a sloppy goal again.
"We keep telling them (the players) that there's no pressure on them."