Mark Yeates twice threatened for Blackpool before the break, with his second effort tipped onto the bar.
A fine run from Stephen Darby set Reid up to fire low into the bottom corner.
Blackpool's Will Aimson saw red in injury time for a second caution after a clash with James Henson.
Defeat sees Blackpool slip to within one spot of the relegation places, with the Seasiders only above Shrewsbury in 21st on goal difference.
Kyel Reid scored the only goal of the game as Bradford City moved to within a point of the play-off spots with victory over relegation-threatened Blackpool at Bloomfield Road.