Evans opened the scoring in the 39th minute after Dale defender Stephen Jordan failed to head clear from Lecsinel Jean-Francois’ ball into the area.
An earlier shot from Evans was parried by David Lucas while United goalkeeper Steve Simonsen made a brave block to deny Nicky Adams.
Rochdale had to make a change in goal at the end of the first half when Lucas received a blow to the head and was taken off on a spinal board after receiving lengthy treatment.
After Evans missed the target from just a few yards out while under pressure from Stephen Darby, Richard Cresswell made it 2-0 when he steered the ball in at the near post following a good cross from Jean-Francois after 57 minutes.
Evans scored his eighth goal in five games with a superb 25-yard free-kick to seal the points for the Blades in the 64th minute before Simonsen kept out efforts from Harry Bunn and Gary Jones.