Parkinson made a double substitute shortly after half-time and the move paid dividends just seven minutes later as former West Ham winger Hines beat three players in a 40-yard run before smartly slotting the ball past goalkeeper Michael Ingham.
Hines was substituted in Bradford's 4-3 defeat at Dagenham last Saturday, and Parkinson said: "Zavon has reacted tremendously well. He has been working with the fitness coach during the week and I am so pleased he got a goal. It will give him a lift.
"Zavon has played in the Premier League and with England's Under-21s, but he has missed his way and I am going to help him to get back on track.
"He is a terrific lad with a big heart and that gives us something to work with. It was a great individual goal he scored. He has got pace and skill, which are big positives."