Jeffrey Schlupp and Max Meyer scored at either end of the first half to reward a professional performance and confirm Palace's passage into the last eight.
Doncaster were competitive throughout and managed to keep Michy Batshuayi goalless on his first Eagles start but lacked the attacking threat to maintain their best FA Cup run in over 60 years.
Roy Hodgson's men, now unbeaten in five matches, will enter Monday's draw as one of six Premier League teams left in the competition.
Palace struck early in their 2-0 fourth-round triumph over Tottenham and did likewise in South Yorkshire as Schlupp, sent through by Luka Milivojevic, drove unerringly across Marko Marosi in the eighth minute for his fifth goal in all competitions this term.
5 - Jeffrey Schlupp has scored five goals in all competitions for Crystal Palace this season; his most in a single campaign since 2011-12 (six for Leicester). Contribution.— OptaJoe (@OptaJoe) February 17, 2019
The visitors had two penalty appeals waved away in quick succession prior to doubling their advantage in first-half added time.
Milivojevic's lofted pass enabled Andros Townsend to nod into Meyer's path for the simplest of close-range headers.
Doncaster offered more going forward after the interval with Liverpool loanee Herbie Kane nodding one half-chance over the crossbar and spearing another shot straight at Wayne Hennessey.
Belgium striker Batshuayi, who cut short a stint at Valencia to join Palace on loan from Chelsea last month, squandered a chance to open his account for the club with around 20 minutes remaining, but the lost opportunity mattered little as Hodgson's side kept alive their hopes of a second final appearance in four seasons.
Key Opta facts:
- Crystal Palace have won away at Doncaster for the first time since August 1960, ending a six game winless run in all competitions (D2 L4).
- Crystal Palace have reached the quarter-final stage of the FA Cup for the second time in the last four seasons; as many as in their previous 33 campaigns.
- Doncaster haven’t beaten top-flight opposition in the FA Cup since January 1985 (1-0 vs QPR), drawing two and losing six since.
- Crystal Palace have scored in their last nine games in all competitions, their longest run since netting in 10 successive games in March 2016.
- No Crystal Palace player has provided more goals (7) or assists (4) than Andros Townsend in all competitions this season.