Anthony Charles' second goal of the season meant Dean Holdsworth won his first home game as Aldershot manager 1-0 while condemning Bradford to their third straight defeat.
Former Newport County boss Holdsworth had drawn his first game in charge at Bury on Saturday to put an end a four-game losing streak.
And buoyed by the new man in the hot seat, the hosts had the better of the first half and deservedly took the lead courtesy of captain Charles' 23rd-minute strike.
The centre-back stayed up from a free-kick and looked more like a striker as he chested the ball down, spun his marker and fired a low shot that beat John McLaughlin at his near post.
Bradford went close to scoring inside 10 minutes through Tom Adeyemi but then rarely tested Aldershot goalkeeper Jamie Young.
The Shots went close to doubling their lead twice through striker Wade Small in the second half and held on to move seven points clear of the relegation zone.
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