The club have earned just their second win since the turn of the year, and it was John Marquis who stole the show with two goals in the second half.
The visitors, though, had an early opening thanks to some decent movement from Tony McMahon on the right-hand side.
The defender attempted to curl the ball into the corner and after a scramble in the box, the ball fell to Timothee Dieng, whose header was cleared off the line.
It took 45 minutes for Bradford goalkeeper Colin Doyle to make a save as he dropped low to the ground to push away Coppinger's strike.
The opportunities in front of goal were few and far between, but the breakthrough was eventually made with 15 minutes remaining on the clock as Niall Mason found Marquis in the box.
The forward, who had scored nine league goals prior to this evening's game, connected with the ball and headed into the back of the net to give the home side the lead.
Bradford had to up the tempo during the closing minutes of the encounter, but despite their efforts they were unable to snatch an all-important goal.
Instead, Marquis punished his opponents further by netting a second in the 92nd minute after Bradford's attack broke down in the middle of the park.
DONCASTER XI (4-1-2-1-2): Marosi; Blair, Wright, Baudry, Mason; Houghton; McCullough (Whiteman 70'), Coppinger; Rowe; Marquis, Kiwomya (Beestin 61')
BRADFORD XI: (3-5-2): Doyle; Kilgallon, Vincelot, Knight-Percival; McMahon, Law, Dieng (Devine 58'), Guy, Robinson; McCartan, Gilliead (Grodowski 59')