The Bantams had not claimed maximum points since New Year’s Day, a run that stretched back ten league outings.
Poleon, however, ensured that dreadful sequence came to an end with his seventh goal of the season.
City rode their luck at times, and especially in the final ten minutes when nerves crept into the home side’s play.
But Bradford held on to end an 82-day wait for three points and, in the process, earn Simon Grayson his first victory since succeeding Stuart McCall on February 11.
It was also enough to nudge the Yorkshire side to within four points of the play-offs, with a game in hand on sixth placed Peterborough United.
The breakthrough came early in the second half. Just three minutes had elapsed when Stephen Warnock played a pass inside to Poleon.
Turning sharply, the City striker then drilled a low shot that gave Tomas Holy no chance in the visitors’ goal.
Poleon should have had a second 16 minutes from time. Lovely approach play by Nicky Law and Alex Gilliead created the chance but the former Leeds United junior made a total hash of his shot.
City could have done with the cushion of a second goal in an nervous finale that saw Colin Doyle save from lively substitute Tom Eaves and Conor Wilkinson head over from a Bradley Garmston cross when it seemed easier to score.
Doyle, having rushed back from Turkey after playing for the Republic of Ireland last night, had also ensured the first half remained goalless with a flying save to deny Lee Martin.
Otherwise, neither goalkeeper had too much to do despite both teams having a spell on top.
Scott Wagstaff wasted Gillingham’s best chance by dragging his shot wide after being picked out unmarked by Bradley Garmston.
For City, Tony McMahon and Dominic Poleon fired well wide when well placed, while Alex Gilliead was unfortunate to see his dangerous cross cut out by Max Ehmer.
As the players left the awful Valley Parade pitch at the break, this was clearly a game up for grabs. Poleon ensured that chance did not go begging to end City’s long, long wait for a victory.