The Bermudan international took his tally to 10 league goals this term, extending the Bantams' unbeaten run to three games while the hosts remain at the foot of League Two.
The visitors started brightly but early efforts from James Hanson and Nathan Doyle failed to beat Shots 'keeper Jamie Young. Wells finally did, though, after latching on to an under hit back-pass from Sonny Bradley before tucking home left-footed from 12 yards after 28 minutes.
It took 35 minutes before the hosts threatened, a corner breaking to Danny Hylton whose shot was blocked on the line, with Scott Donnelly missing the chance to turn in the rebound.
A minute later Wells dinked an effort wide but doubled his tally on 39 minutes, tapping home after Young had parried Hanson's effort straight into his path.
The visitors continued to press after the break, Hanson saw an effort from the edge of the box saved by Young before Wells was denied a hat-trick when his acrobatic bicycle kick hit a post late on.