Neil Woods’s side claimed all three points thanks to goals from Cameron Painter and Lennon Stead.
The young mariners were looking to bounce back this weekend after a disappointing opening-day 4-1 defeat to Doncaster Rovers.
Town could have opened the scoring inside a minute when Brandon McPherson forced the opposition keeper into a smart save.
The game was closely contested with both teams forcing saves from the goalkeepers.
But Painter opened the scoring for the Mariners when his cross sailed over the goalkeeper and into the net to give Town a 1-0 lead just before half time.
Town came out on the front foot in the second half and created a few openings whilst keeping the Bantams at bay.
And Woods’s side doubled their lead in the 65th minute after some good play saw Stead lift the ball over the goalkeeper in calm fashion.
Town went close again when they hit the post but Bradford hung in there and did reply with a header from an inch-perfect cross.
Town managed to hold out for their first win of the season as it ended 2-1.
The young Mariners are away at Burton Albion on Saturday (12pm).