Miles' second four minutes from time sealed the win when Michael Symes' ball across the face of goal found the wideman and he finished from an acute angle.
It halted a run of three games without a win for play-off chasing Stanley, while former England Under-21 coach Taylor will know he has work to do with a Bradford side who have now won just once in their last six outings.
They created very few chances despite fielding a three pronged attack and Accrington goalkeeper Ian Dunbavin was a spectator for long periods.
The visitors' best chance fell to top scorer James Hanson after the break but he blazed over from six yards following Simon Ramsden's free-kick delivery.
Source: Team Talk
Source: Team Talk