After a Hanson opener in the first period and then an Alan Sheehan penalty just after the break had twice put Parkinson's side in front, Coventry skipper Reda Johnson's second equaliser of the match with only one minute of normal time remaining looked to have snatched a point for the visitors.
Barely sixty seconds later, however, inventive play down City's right flank by Jason Kennedy gave Hanson the opportunity to head in the winner and send the home crowd into ecstasy.
Parkinson said: "I thought it was a great game - very entertaining for both teams and both sets of supporters. It was a bit similar to the game we played against them here at home last season.
"I felt it was another great advert for the division.
"Sometimes opening day games can be cagey affairs but some of the football played out there was very, very good.
"At one stage it looked like we might have to take a point, but I felt we deservedly won the game in the end.
"We wanted to put a marker down in front of our own supporters today (Saturday). We wanted to show them what we will be all about this season and how much it means to the players to wear the Bradford City shirt.
"You need to show commitment, drive and passion to wear the Bradford City shirt, and I feel the lads did that.
"It is unfair to single anybody out really because I felt one to eleven we were very good today.
"We have spoken to the lads about the atmosphere the fans can generate in this ground but, equally, we know that the players can do their bit to inspire that passion from the supporters.
"The first run, the first tackle, the first cross, the first header was always going to be important today as it lifted the crowd and, as we know, once you get this crowd out of their seats, they can make a real noise for us.
"The first game of the season, especially the first home game, is all about sending the fans home with a positive mindset about the season ahead.
"I think, like me, they will know now that we have the nucleus of a good squad. Obviously we know that there is still work to do in terms of strengthening the squad but the core of the group is good.
"The first three points on the board is always important. What we will be doing as a squad, however, is making sure we don't think we have cracked it after just one game.
"There is a lot of things we can improve on.
"We will get back to work Monday morning and look to improve again."