Jason Walker levelled the score with a header just four minutes later but Ryan James put the visitors back in front after the break with a 20-yard shot.
Craig Nelthorpe secured Barrow's point with a left-footed free-kick after a foul on Carlos Logan by Billy Crowther.
Barrow: Tomlinson, Spender, Pearson, Bolland, Jelleyman, Rutherford, Hulbert, Bond, Nelthorpe, Walker (Logan 71), Shaw (Bowery 29). Subs Not Used: Deasy, Boyd, Sheridan.
Booked: Nelthorpe.
Goals: Walker 19, Nelthorpe 77.
Grays Athletic: Robinson, Bunce, Hoyte, Crowther, Mawer, Cissoko, Agumbar, Harley, Bingham, Rnkovic, James. Subs Not Used: Edwards, Beavan, Mallmann, Graham, Logombe.
Booked: James.
Goals: Rnkovic 15, James 72.
Att: 863
Ref: P Wright (Southport).
Source: BBC Sport
Source: BBC Sport