The Bantams claimed all three npower League Two points courtesy of goals from Kyel Reid and Craig Fagan, despite falling behind to Danny Stevens' opener for the hosts.
The win ended the Gulls' run of seven straight successes, and Parkinson was delighted with the attitude and application shown by his squad at Plainmoor.
"We came here knowing we had a match on our hands," he said. "There was a torrential downpour at the start and we knew we were against a team with probably the best record of any team in all four divisions of late. I said to the players: 'what a challenge'.
"I knew if we stuck to the game plan and were disciplined in the way we went about our task I thought we had a good chance of winning, I really did.
"We have got a lot of belief in the players but only when we do the jobs we ask them to do. We are a good team and we can beat teams above us if we stick to the game plan."
Bradford last week