The Wales striker twice equalised for Danny Wilson’s Blades in the first half but it was a former United player, Jon-Paul McGovern, who snatched the winner.
Francis Zoko got the hosts off the mark with his fourth goal in five games, when he beat Steve Simonson after a neat bit of skill.
But Sheffield United levelled within minutes when Stephen Quinn’s free-kick was headed into the path of Evans by Harry Maguire, and Evans made no mistake.
An exciting opening showed no sign of relenting as Carlisle retook the lead on 15 minutes when Zoko was left with a simple tap-in after an unselfish header back across goal by Lee Miller.
Back came the Blades who equalised again on the stroke of half-time through their top scorer Evans.
The striker had a free-kick blocked and although Chris Porter fired the rebound straight at a Carlisle defender, Evans finally found the net at the third time of asking.
But United fell behind for a third time 19 minutes from time.
McGovern, who played for both Sheffield clubs, exchanged passes with Miller and fired home to restore Carlisle’s advantage.
Sheffield United drop out of the top two in League One after this defeat.
For a report and reaction read Tuesday’s Yorkshire Post.