Accrington took their chances in a scrappy and difficult to watch game and that was enough to send the Cumbrians home with plenty to think about from what has been a disappointing Easter weekend.
A huge ball forward from Hanford brought an early corner for the Blues, as a Grainger cross was blocked, but Jones did well to clear as O'Hanlon tried to get a flick.
The sides took time to settle on a tense afternoon but Accrington suggested better was to come when Joyce picked out Maguire with his back to goal. He fed it wide but Gilchrist had to stretch and his header was easy for the keeper to grasp.
United had a good spell of their own sparked by Grainger when he clipped a low corner to the near post. Archibald-Henville recovered the half clearance but Grainger, who had dropped deep, had to volley on his weaker foot and his effort was blocked. It eventually squirmed through to Archibald-Henville but his touch took it agonisingly wide as Davies dived to cover.
Stanley grabbed the lead from nowhere courtesy of a fantastic run from Mingoia as he cut in from the right flank. He beat two before picking his spot as Hanford raced off his line to try to make the block.
Potts dragged a shot wide as Carlisle struggled to get a foothold in the game and the same player sliced a volley wide from 22 yards when Beck nodded an Atkinson cross into his path.
And there was more frustration for the Cumbrians on the stroke of half time when the ball rolled to Dempsey from a long throw from Atkinson. He took a touch but he couldn't find the target as he pumped his effort over the bar.
Carlisle almost drew level after the break when a good move down the left brought a flick from Dempsey. Beck came in on the angle and drilled a low shot across the face of goal and he was disappointed to see it bounce just past the upright.
A run of corners followed but Accrington were able to calm things down when Beck arrived late to put a diving header behind for a goal kick. It was better, though, from the visitors and O'Hanlon found the side netting when he spun on another long throw from Grainger. He put it past Davies but it was just an inch the wrong side of the target.
United thought they'd done the job just before the hour when Potts won his header in midfield. Dempsey ran away with it and his cut back was perfect for Wyke. He let one go from 16 yards but Jones and Hunt combined to make an excellent block.
The good second half work was wiped out when Carlisle fell asleep for an Accrington set piece. Bruna was given acres of space to receive it on the left flank and his flat cross found Windass unmarked on the edge of the area. A crisp volley left Hanford with no chance.
The third goal came when Bruna appeared to miskick his corner delivery. It was allowed to run on and Seamus Conneely took a cheeky touch to send it through Hanford's legs and over the line.
Dempsey shot wide, and Wyke blazed over from eight yards as United tried to salvage something, but Accrington went close again when Naismith took charge of a 22 yard free kick. He struck it sweetly but it shaved the outside of the post.
Accrington saw the game out in relative comfort with Mingoia and Naismith sending shots over the bar, even though Dempsey grabbed a late consolation deep into time added on.
Accrington - Mingoia (24), Windass (62), Conneely (65)
United - Dempsey (90)
United - Dempsey (38)
Accrington Stanley - Davies, Buxton (Liddle 73), Joyce, Jones, Windass, Mingoia, Hunt, Gilchrist (Conneely 59), Maguire, Bruna (Naismith 73), Atkinson. Subs - Warner, McCartan, Barry, Bowerman.
Carlisle United - Hanford, Atkinson, Archibald-Henville, O'Hanlon, Grainger, Potts (Dicker 81), Kennedy, Thirlwell (Beck 36), Dempsey, Kearns (Paynter 69), Wyke. Subs - Gillespie, Buddle, Young, Corry.
Referee - Mr Michael Bull
Attendance - 2,274 (939 away fans)