Yohan Cabaye and Frazer Campbell ensured the Premier League side progressed to the semi-finals of the competition when he struck home from 12 yards
Cabaye converted from the spot in the 86th minute after Jake Cooper had needlessly hauled down Yannick Bolasie, with the Reading defender picking up a second yellow card from referee Mike Dean.
The visitors made sure of the win in injury time, substitute Campbell finishing at the second attempt after his initial effort had struck a post.
Defeat was particularly harsh on Ali Al-Habsi, with the Reading goalkeeper turning in an inspired display to put his side within touching distance of a replay at Selhurst Park.
However, Palace - who are on a run of 12 Premier League games without a victory - secured a trip to Wembley at the expense of the club where manager Alan Pardew started his managerial career.
The visitors, the only team in England's top four divisions yet to register a league win in 2016, seem to be up for the cup. They had knocked out top-flight rivals Southampton, Stoke City and Tottenham to reach the sixth round of the competition.
However, they found themselves up against a goalkeeper in fantastic form, with Al-Habsi first called upon on the half-hour mark to palm away a free-kick from Cabaye, although he was fortunate Emmanuel Adebayor's curling effort when clean through was aimed straight at him.
The Oman international - an FA Cup winner during his time at Wigan Athletic - then saw Joe Ledley blaze a rebound over the bar after Bolasie's initial effort had been blocked.
Reading's best chance before the break stemmed from a Wayne Hennessey error, as the goalkeeper palmed a deep cross straight to Ola John.
But rather than square the ball to the waiting Stephen Quinn, the on-loan Benfica forward fired into the side netting from a tight angle.
Al-Habsi continued to keep Palace at bay in the second half, leaping up in the 54th minute to keep out Mile Jedinak's powerful header from Cabaye's free-kick with his left hand.
John planted a diving header straight at Hennessey, allowing the Wales international to keep the ball out with his feet, and it seemed the game would end goalless.
Instead, Cooper's rash decision to reach out an arm and bring down Bolasie allowed Cabaye the chance to break the deadlock. Al-Habsi came close to saving the spot-kick, but the power of the strike made sure it found the net.
Campbell's effort in added time killed off any lingering hopes Reading had of making it through to the last four for a second successive season, with Pardew - a semi-final goalscorer in Palace's run to the 1990 final - closing in on more cup magic this season.