On a difficult playing surface at Bloomfield Road, City deservedly ran out winners thanks to Kyel Reid's strike early into the second half in front of an estimated 3,000 travelling supporters.
Reid's match-winner - a fine first time finish from inside the area - came about thanks to a purposeful from Stephen Darby which saw the City skipper surge past four Blackpool players before setting up the winger.
On top of Reid's effort - his third goal of the season - another important highlight in the match for Parkinson's men saw City shot-stopper Ben Williams produce an outstanding full stretch save to tip former Bantam Mark Yeates' curling strike onto the bar on the stroke of half time.
Parkinson said: "We did the job today (Saturday) - we were very professional.
"We did the right things in the right areas, and it is a terrific away victory for us.
"As the game wore on, we got stronger and stronger.
"It was a moment of inspiration from Darbs for the goal - a great run and pass from Stephen - and it is a fantastic finish from Reidy.
"Before that, it was a top-class save from Ben in the first half.
"We were right behind it and I don't know how he got his finger-tips onto it.
"Saves like that are as important as the goal. It got us into half-time level when we could have gone behind and given Blackpool a lift.
"We had fantastic support again, the lads seem to thrive under the pressure of having to perform in front of the bigger away crowds.
"Hopefully we have sent them home happy."
City sadly had to play Saturday's match at Bloomfield Road without assistant manager Steve Parkin following the recent passing of his mother.
Parkinson added: "Steve has lost his mother this afternoon. I really feel for him and his family.
"Our thoughts are definitely with him at this difficult time.
"We have missed him today but we did everything we could to bring the three points back for him.
"He is a huge part of what we are trying to achieve here at Bradford City."
The only downside to City's victory at Blackpool was injuries to Reece Burke and Steven Davies towards the end of the match. Wes Thomas also picked up a knock during the second period.
Parkinson continued: "It is a real shame for Steve, he has been looking sharp. It is his knee that he has injured but we don't know the true extent just yet.
"Wes has got a whack on his calf and Reece has twisted his ankle again, similar to what he did before.
"Hopefully none of them are too serious but we won't know until probably Sunday/Monday.
"It does mean, however, that those players not involved today will now get an opportunity.
"That is why we have a squad that is strong and ready to compete."
Following Saturday's win over Blackpool, City now quickly turn their attentions to their home fixture with bottom-of-the-table Colchester United.
Parkinson said: "The lads are really pleased with their work but it is eyes down and ready to go again on Tuesday night.
"Teams at the bottom are fighting and kicking for every ball at the moment. The minute you give anything less than 100% for a game, you leave yourself open to trouble.
"Blackpool were fighting with us today for every ball, and Colchester will come to us on Tuesday and do exactly the same.
"We have to show the same commitment and resiliency as we did at Blackpool today."