Substitute Hector Mackie grabbed a late winner for Bath over fellow mid-table outfit Grimsby.
City's Marley Watkins latched on to Lee Phillips' cross 12 yards out and found the top corner to open the scoring.
The Mariners flew out of the traps after the break and were level on the hour when Michael Coulson's fine effort from the left went in to make it 1-1.
Mackie secured the winner five minutes from time when he hammered right-footed into the top corner.
Bath City: Robinson, Simpson, Jombati, Jones, Clough, Murray (Mackie 73), Connolly, Burnell, Canham, Watkins (Rollo 90), Phillips. Subs Not Used: Borhy, Henry, Mohamed.
Booked: Clough.
Goals: Watkins 32, Mackie 85.
Grimsby: Croudson, Ridley, Sinclair, Atkinson, Watt, Coulson, Leary, Wood, Eagle, Duffy (Peacock 82), Connell.
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Subs Not Used: Arthur, Makofo, Gray, Thanoj.
Booked: Wood, Ridley, Atkinson.
Goals: Coulson 60.
Att: 1,808
Ref: Ian Cooper (Kent).
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