But the hosts had Billy Crowther sent off for a second yellow card and Malvin Kanara headed Barrow 2-1 ahead.
Jamie Slabber seemed to have earned Grays an unlikely win with a fine low shot and a close-range effort that made it 3-2 but Jones salvaged a late draw.
Grays remain three points from safety at the bottom of the Blue Square Premier while Barrow maintain their mid-table position in 16th spot.
Grays Athletic: Edwards, Mawer, Uddin, Crowther, Bunce, Graham, Robson, Leahy (Logombe 38), Poole, Onibuje (Charge 80), Slabber. Subs Not Used: Anderson, Rnkovic, Agumbar.
Sent Off: Crowther (37).
Booked: Bunce, Crowther, Onibuje, Logombe.
Goals: Onibuje 14, Slabber 51, 61.
Barrow: Tomlinson, Dugdale, Jones, Pearson, Jelleyman, Kamara, Bond, Hulbert (Boyd 72), Rutherford (Logan 65), Shaw (Cook 79), Walker. Subs Not Used: Deasy, Sheridan.
Booked: Jones.
Goals: Shaw 33, Kamara 38, Jones 86.
Att: 736.
Ref: R Fletcher (Derbyshire).
Source: BBC Sport
Source: BBC Sport