Goals from Hogan Ephraim and Neil Kilkenny booked Leeds place in the Johnstone`s Paint Northern Area final.
Leeds made nine changes from Saturday for the game including a first start for David Martin in goal who joined from Liverpool on loan in November.
Ryan had the first chance of the game for Stanley after Leeds gave the ball away in midfield, his long range shot was saved at the second attempt by Martin.
Hogan Ephraim who had started the game lively gave Leeds the lead inside the first ten minutes, a good ball by Kilkenny released Ephraim down the left who cut inside and his shot took a huge deflection to beat the keeper.
In a quite first quarter, Tresor Kandol had Leeds next decent effort when Ephraim put him through on goal, his shot was saved by Bouzanis when he really should have scored.
Stanley were trying to get back on level terms and Richard Naylor almost put through his own goal from a cross into the box.
Accrington`s best chance of the half fell to Symes whose free header was straight at Martin.
Snodgrass was next to have a go at goal but his shot never troubled the Stanley keeper.
Leeds took a slender lead into the half time break with the tie far from won.
Leeds doubled the lead early in the second half when Ephraim`s cross was met by Kilkenny whose diving header found the back of the net.
Simon Grayson decided to make changes with twenty minutes remaining, Sam Vokes and Max Gradel replaced Mike Grella and Tresor Kandol.
Vokes almost scored within minutes when he was one on one with Bouzanis but wasted the chance.
Accrington were still refusing to lie down and John Miles hit the post.
Sean McConville then had a great chance for the visitors when one on one with Martin but he fired over the bar.
Stanley continued to press and again hit the post with Miles just failing to beat Naylor to the rebound.
Gradel had Leeds best effort for a while when his shot was turned over by Bouzanis.
Miles had another good chance for Stanley but shot over with Martin on the floor.
Leeds will now face Carlisle United in the Northern Area final in a two-legged tie; the first leg will take place week commencing 18th January, with the second leg week commencing 15th February.
D. Martin, Crowe, Naylor, Michalik, Hughes, Snodgrass, Prutton, Kilkenny, Ephraim, Kandol, Grella
Ankergren, Doyle, Vokes, Gradel, Kisnorbo
Bouzanis, Kempson, Edwards, Winnard, Joyce, Proctor, Grant, Ryan, Symes, Murphy, Kee
Miles, G. King, Flynn, McConville, Dunbavin
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