Bath and Barrow remain near the foot of the table after they shared the spoils at Twerton Park.
Barrow made the breakthrough when the ball sat up nicely for midfielder Mike Pearson who volleyed home into the bottom-left corner from 12 yards.
The Cumbrian outfit almost scored a second when Andy Cook forced a fine save from Bath keeper Ryan Robinson.
The home side levelled when Marc Canham's corner was headed home from close range by Darren Edwards.
Barrow joint-boss Dave Bayliss told BBC Radio Cumbria:
"We were the better side from start to finish, we created a lot of good chances.
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"It's the most comfortable we've been defensively for three or four games, the debutant Shaun Pearson hasn't had a save to make.
"But one lapse of concentration has cost us - we've not been strong enough at a set-piece.
"The lads are gutted because they've worked their socks off and should have come away with three points - it's two massive points dropped."
Bath City: Robinson, Simpson, Jones, Webb, Rollo, Mackie (Reid 61), Harris (Badman 76), Connolly, Canham, Edwards (Phillips 79), Mohamed. Subs Not Used: Coupe, Hart.
Booked: Canham.
Goals: Edwards 77.
Barrow: Shaun Pearson, Spender, Mike Pearson, Bolland, Edwards, Wiles, Hulbert, Boyd, Donnelly, Owen, Walker (Cook 68). Subs Not Used: Blundell, Sheridan, Forrest, Nicholas.
Booked: Bolland, Owen.
Goals: Mike Pearson 32.
Att: 875
Ref: C Powell (Dorset).
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