The knock-out tie was won with two goals at either end of the first half, with Jeffrey Schlupp and Max Meyer combining to give the Eagles their deserved victory.
To start, playing under shade from the beating Yorkshire sun, the day's opening exchanges were as tepid as the weather until, as the match neared the end of its first 10 minutes, the Eagles' Schlupp emphatically sparked things into life.
Picking up the ball within his own half, the Palace midfielder drove with purpose towards the Rovers' backline and, looking up, fired across the box beyond the out-stretched arms of Marko Marosi to open the London side's account.
However, despite having grasped an early lead, Palace were adeptly kept on the back foot as the home team pressed high and with pace to earn themselves a succession of ultimately unsuccessful corners.
The Eagles attempted to lash back at Doncaster's spell of pressure when Jordan Ayew picked up the ball in their box, turned and did well to send a strike at goal. Shot-stopper Marosi, however, was in place to hold his venomous effort.
At the other end of the pitch, the Rovers refused to change their tactical approach and Alfie May launched a shot at the visitor's goal which sailed to safety over Wayne Hennessey's bar.
Later, following Meyer's deflected effort, Palace came close to scoring from a 27th-minute corner as Scott Dann put power behind a header only to see his attempt glance out of touch, contentiously stroking the arm of Danny Andrew as it did.
For the second time in five minutes, Palace were then frustrated to see nothing awarded by referee Mike Dean when a ball from a Palace defender, this time Patrick van Aanholt, struck the arm of a Doncaster defender, this time Paul Downing, in the Rovers' box.
Shortly after, though, Palace weren't to need refereeing decisions to double their advantage when, seconds before Dean blew his whistle to conclude the first-half's solitary added minute, the Eagles doubled their lead through Meyer, who, facing an unguarded half of goal, nodded home to extend his side's advantage from a looping Andros Townsend header across the box.
Opening the second half, it was Doncaster who were to threaten first when Benjamin Whiteman launched a shot at goal which, swerving, was beaten away by Hennessey before May headed just over from the following corner much to the relief of Palace's 3,000 travelling fans.
Building on their momentum, Doncaster again forced south Londoners' breath to be held when club veteran James Coppinger rifled a shot which deflected off Martin Kelly and just over Hennessey's bar. Ali Crawford, similarly, went for a heroic opener to the Rovers' account, however his strike was wildly high.
The squandered chances weren't to discontinue as a mass of bodies in the Palace box all looked on as on-loan Herbie Kane sent a header over the Eagles' woodwork, but it was Doncaster who were then in the ascendancy.
Switching to a four-man midfield with the arrival of Cheikhou Kouyate, Palace looked to solidify and terminate Doncaster's bout of pressure and, with the vociferous support of Croydon's travelling faithful, the approach seemed to work.
Michy Batshuayi came tantalisingly close to adding a third to the afternoon's total when, running head-on into the box, his touch was too heavy and, almost one-on-one with Marosi, the Rovers 'keeper was able to smother the ball to safety.
Seconds later, Meyer deftly brought down a loose ball from Batshuayi's cleared header, however the drilled resulting effort was sent out of play.
With just over 10 minutes left to work his side's way back into the game, John Marquis angled an effort at Hennessey's near-post, but the 32-year-old shot-stopper was equal to it and stood firmly behind the ball.
Unable to pull off a late comeback and bereft following their nullified second-half surge, Doncaster were beaten at the final whistle and, at their expense, Crystal Palace pull themselves just one game away from Wembley.
Palace: Hennessey, Ward, Kelly, Dann, Van Aanholt, Milivojevic, Meyer, Schlupp, Townsend (McArthur 80), Ayew (Kouyate 60), Batshuayi (Benteke 75).
Subs not used: Guaita, Woods, Tomkins, Riedewald.
Doncaster: Marosi, Blair, Downing, Anderson, Andrew, Whiteman, Kane, Crawford (Rowe 64), May (Boocock 90), Marquis, Coppinger (Sadlier 64).
Subs not used: Jones, Wright, Butler, Lewis.
Post-match reaction is set to follow shortly. Return to cpfc.co.uk to read it!