Arsene Wenger's men, who required penalties to see off Wigan Athletic at this stage last year, struggled to find the momentum that has seen them embark on an eight-match winning run.
Nevertheless, Alexis Sanchez put the holders in front six minutes before the break with a cool finish having been fed by Mesut Ozil.
Arsenal hit the woodwork twice as they looked to avoid extra-time - once via a superb save from Federici - but the Australia international will have wanted the ground to swallow him whole when he allowed another Sanchez effort to squirm underneath him at the end of the first period of additional time, dashing Reading hopes of a first final.
Arsenal welcomed back defender Mathieu Debuchy for his first appearance since January following shoulder surgery and, after a bright start from Reading, the holders began probing their opponents' back line.
Having seen an earlier chance fizzle out courtesy of a heavy touch, Sanchez made no mistake with his next opportunity, showing great composure in the box to bring down an Ozil pass, see off his marker and send the ball between Federici's legs.
Gabriel Paulista came off the bench for Mertesacker shortly after the hour mark and one of his first contributions was to draw a fantastic save from Federici, who pushed the Arsenal defender's header onto his crossbar.
Chalobah tried his luck from 20 yards out with seven minutes left of normal time, forcing Szczesny into an unconvincing save, before Aaron Ramsey – Arsenal's goal hero when they won last season's competition – hit the post after forcing his way into the Reading box under pressure from Obita.
The Reading stopper was unable to hold the low strike and somehow allowed the ball to sneak through his legs and over the line, sending Arsenal into a final clash with the winner of Sunday's semi-final between Liverpool and Aston Villa.
