Evans gave the Bantams the lead with style early on as he curled home from 20 yards into the bottom corner.
The Shripmers fought back and Ryan Leonard forced Bradford goalkeeper Ben Williams into a fine save with a fierce effort from long-range.
The hosts almost restored parity when Tyrone Barnett volleyed against the crossbar but Bradford held on.
Bradford City made sure of a League One play-off spot as they beat Southend United thanks to Lee Evans' early goal.