Second half strikes by Aaron Mclean and Gary Liddle within the space of two minutes secured the Bantams a deserved victory after their earlier efforts in the game had been repelled by Crewe.
City could have twice opened the scoring in the first half when Mclean and Billy Clarke both saw efforts cleared off the line. Parkinson's men also had twelve corners in an opening period that they dominated almost from start to finish.
City's efforts in the game were finally rewarded eighteen minutes from the end, however, when Mclean converted from Mark Yeates' cross to break the deadlock. Liddle then netted his first for the club with a fine finish from just outside the box shortly afterwards to secure the points.
Parkinson said: "We had a lot of domination in the first half - twelve corners, balls cleared off the line - and we just said to the lads at half time to just keep going.
"There were one or two things we looked to change for the second half but in the main we just wanted them to keep going.
"We were looking to eventually wear them down and for someone to take a chance, and thankfully some great play on the left by Mark Yeates and a good finish by Aaron (Mclean) has settled everyone down.
"This game could have been a tricky one for us given our recent home form and Crewe's results going into this game perhaps leading to greater expectation from us, but I felt the lads handled it really well.
"The lads were determined to get a result today, and it was important that we gave our fans something to smile about because our last few results here (Coral Windows Stadium) haven't gone our way."
With Alan Sheehan, Filipe Morais and the fit-again Andrew Davies all recalled into the side, Parkinson moved away from his usual diamond formation in midfield to instead go with a more traditional 4-4-2 shape.
The changes meant Christopher Routis, James Meredith and Billy Knott all moving down to the bench.
Parkinson: "We just felt we had to change the dynamics of the team slightly and excite the crowd more.
"That meant getting more crosses into the box, more attempts on goal.
"With regards the changes, I thought Chris (Routis), Mezzer (James Meredith) and Billy Knott's attitude was superb after being told they weren't in the side for this game.
"That is important to see. Chris and Mezzer in particular have been playing well recently and can count themselves a bit unlucky to be left out of the team.
"Billy (Knott) hadn't had his best game last weekend (vs Port Vale) but he showed a great attitude when he came on.
"We always stress to the lads that it is a squad game. You get disappointed when you are left out of the team - that is natural - but we ask players to respond in the right way. Those three certainly did that for us.
"Davo (Andrew Davies) played well, he looked strong and committed as ever against a tricky player in (Marcus) Haber."