Wells scored the winner after 24 minutes with his 19th goal of the season and his sixth in five matches between the teams.
Visiting goalkeeper Lee Nicholls failed to deal with a long pass out of defence from Garry Thompson and when Coventry loanee Nathan Cameron tried to head the ball out of play, Wells chased it and turned into the net.
Bradford had chances to increase their lead as they dominated the second half, but were denied by Nicholls, who made diving saves from Kyel Reid and skipper Gary Jones while James Hanson was twice off target when well placed.
Northampton, who were dangerous from set pieces, almost made the home side pay for their misses when Jon McLaughlin was forced to make a superb diving save to keep out Ben Harding's shot in the 74th minute.
- Sports & Recreation