An early opener from Francois Zoko - his first goal for the Bantams - was enough to secure all three points for Parkinson's men and keep them in touch of the Play-Off places.
The win, in fact, moved City to within one point of sixth-placed Doncaster Rovers with a game in hand.
Following City's cup victory over Sunderland in the fifth round last month, Parkinson said that the target for City had always been to go into this Saturday's last eight tie with Reading at the Coral Windows Stadium still firmly in the hunt for a Play-Off spot.
With that now certainly the case following the Crawley victory, Parkinson believes his side can truly savour what should be an exciting few days for the club.
Parkinson said: "It is similar to when we beat Milton Keynes Dons on the Monday night before the Sunderland tie, that was a huge win for us.
"This is a big three points for us.
"We can enjoy the build up now and look forward to what will be a cracking atmosphere here at the Coral Windows Stadium on Saturday.
"A F.A Cup Quarter Final at home in front of a full house with three league points already in the bag, it doesn't get much better than that.
"After losing two games on the road (Swindon Town and Peterborough United), it was so important we got back to winning ways tonight (Tuesday).
"We were desperate to get the game on. It was touch and go at one point with the weather forecast.
"Thankfully, the weather wasn't as bad as forecast. Credit to (Head Groundsman) Mick Doyle for getting the game on and to the referee (Darren Drysdale) for not making too big a deal about the conditions."
After thirteen previous substitute appearances, Zoko's Crawley match-winner came on his first full start for the City.
The Ivorian's inclusion in Tuesday's line up was one of seven changes made by Parkinson for the loss at Peterborough last Saturday.
Parkinson added: "It was important for Francois to get that first goal for us.
"He has deserved that. He has been great in the way he has trained with us since he's arrived and the way he is around the other lads.
"He has been very unlucky previously with chances that have been kicked off the line or hit the post in other matches. He worked very hard tonight though and his performance deserved a goal.
"The reaction from the lads when he came into the dressing room said it all. They obviously appreciate the goal but they also understand the work-rate and effort he has put in tonight and during the earlier parts of the season."