The visitors were two down by half-time after strikes from Peter Thorne and Joe Colbeck, but Bradford lost their way after Jackson made them pay for some sloppy defending five minutes after the break.
Promotion-chasing Bradford still had their chances to wrap up the win and, when Bentley was red-carded for a full-bloodied challenge on Paul McLaren after 58 minutes, the home side should have pressed home their advantage.
But dozy City were caught napping at the back again with seven minutes left and Jackson powered onto Nicky Southall's pass to fire a cool finish beyond keeper Rhys Evans.
Jackson limped out of the action having been injured in the act of scoring the equaliser and Mark Stimson's side had to survive some late scares as City pressed forward trying to save their blushes.
A mistake by left-back John Nutter gave Colbeck another sight of the Gillingham goal deep in injury time, but his fierce drive was brilliantly tipped away by keeper Simon Royce.
Even then there was still time for more late drama as Colbeck's corner was headed onto the Gillingham crossbar by Bradford skipper Graeme Lee and when the rebound fell to substitute Willy Topp the Chilean fired his volley over the bar.
It was a remarkable turnaround after City overcame a slow start to hit the visitors with two goals in the opening period.
League Two leading scorer Thorne fired City ahead after 20 minutes with his 10th of the season after a Michael Boulding header came back off the post.
And, although Colbeck doubled Bradford's advantage with a stunning right-shot from the edge of the box in the dying seconds of the half, Gillingham never let their heads drop.
Five minutes after the break, Jackson poached his first with a neat finish after a scramble in the Bradford box and, after Thorne and Omar Daley wasted good openings for the Bantams, the visitors dug deep to earn a hard-fought point.