Carsley's sweetly curled second-half free-kick earned an uneasy progression into the next round. Substitute Marcus Bent sealed the tie a minute from time.
Everton boss David Moyes rewarded Saturday's matchwinner Duncan Ferguson against the Championship side with a start upfront alongside pacy youngster Leon Osman.
Moyes also rested Alan Stubbs, with Thomas Gravesen and Bent taking a place on the bench.
The game kicked off ten minutes late due to crowd congestion as the hordes of travelling Lancastrians piled into Goodison Park.
Not overawed by the Blues' lofty Premiership position, the combative visitors seemed intent on attacking from the outset and enjoyed better of the opening exchanges.
Richard Cresswell was unlucky with the ricochet as he charged down Richard Wright's nonchalant clearance on ten minutes.
Everton responded with a succession of corners, with Ferguson his usual meddlesome self. His mighty leap on 17 minutes provided Everton's first effort on goal, but his header was off-target.
Ferguson slammed the ball in the net midway through the half, but the whistle had blown for an earlier foul on Osman.
Kevin Kilbane and the gangly Scot again came close with headers as the halfway mark approached.
Ferguson squandered the best chance of the half, on 41 minutes, when put through by Osman, but Gavin Ward came off his line to make a smart save.
Everton continued to unlock the visitors' defence with concerning regularity. This time James McFadden burst clear to lob the oncoming Ward, but his shot drifted agonisingly wide.
The Blues started the second period in much the same vein, with the tiring visitors forced into fouling the rampant Merseysiders.
Osman was clattered on 51 minutes and Preston paid the ultimate price when Carsley curled in a beautiful free-kick that Ward couldn't keep out.
Amazingly Preston hit the net midway through the half, but their joy was short-lived when Youl Mawane's goal was ruled out for a foul in the box.
But they continued to press and a well-worked free-kick saw David Healy's low shot smartly turned around the post by Wright.
Moyes' woes were increased when Carsley was given a straight red card for a disgraceful elbow on substitute Eric Skora on 73 minutes, as tempers boiled over.
McFadden squandered the easiest of chances to settle the tie with just five minutes left on the clock. Kilbane found the Scot in space, but he skyed his effort from barely six yards.
It became irrelevant when Bent sealed proceedings with his first touch after coming on for Ferguson with just a minute left. It was a carbon copy of the chance McFadden had blown a minute earlier.