First half goals from Kyel Reid and Reece Burke gave City a deserved half-time lead after a superb performance from Parkinson's men in the opening period.
Burton had more of a say in the match after the break but City held firm and could have even extended their lead but Tony McMahon's penalty eleven minutes from time was saved by former Bantams shot-stopper Jon McLaughlin.
The victory moves City up into seventh in the Sky Bet League 1 table and just outside the Play-Off places on goal difference alone.
The win was also a fitting way for the Bantams to redeem themselves in front of their own supporters following the disappointing defeat to Colchester United in the club's previous home match just seven days earlier.
Parkinson said: "A week is a long time in football. This time last week, we were so disappointed with the way we played.
"All you can do after a result like that is try and respond in the right way though. It was very important that we put in a good display in front of our home fans tonight (Tuesday). The lads were excellent.
"We probably started in the same manner that we did against Colchester United last Tuesday but this time the players knew it was important to sustain it.
"The lads knew they had to stick to their task throughout the game, and they did their jobs terrifically well.
"This result just shows we can achieve. We've beaten top of the league two-nil and it could have been three with the penalty.
"Burton are a top side and they were always going to have a response in the second period but we came through it all and defended very well right from the front.
"It was a very solid and committed display.
"Tonight was like a bonus match for us with it being our game in hand.
"There was almost a cup tie atmosphere around the ground because I think the fans could sense the importance of this fixture.
"We knew the top-of-the-table side were coming into town and that we had to be at our best, and I think we were close to that."
City's eye-catching display against title-chasing Burton was helped in no small part by the hard-working duo of Jamie Proctor and Billy Clarke, both of whom were recalled in attack by Parkinson for the rearranged fixture.
James Hanson missed the match altogether due to illness, while Parkinson decided to name Wes Thomas among his substitutes for the game.
Parkinson added: "They were both terrific. Proctor has come into the side tonight and ran himself into the ground.
"He's ran the channels, he's won headers and he's held the ball up well.
"Clarkey gives us the different dimension up there. He's missed a bit of football for us this season through injury but I've said all along what a key player he is for us.
"He has that bit of craft and quality on the ball, and he's played his part in both goals.
"It is frustrating for any player to be left out of the team but all you can do when you do get your chance is try and take it like those two have done tonight."
Reid was another impressive performer for City on the night despite suffering with illness himself during the course of the game.
Parkinson continued: "We've had a bit of illness in the camp.
"Hanson was ruled out tonight because of it and Mezza (James Meredith) had it at the weekend.
"Kyel was struggling a bit at half-time but he was determined to stay on.
"What a fantastic goal he has scored - this is the fittest I've seen him in all the time I've worked with him. He is looking physically very strong."