Jefferson Lerma and Romain Esse were then introduced for the final half-an-hour, with Turner required to make another alert save to keep out the lively Sharp.
Doncaster refused to let the game drift away, the lively Molyneux firing just over bar after cutting in from the right channel.
But they eventually ran out steam, Palace seeing out four minutes of injury time with ease, as Glasner gave Matheus França a return from the bench – his first competitive minutes for the club since 2nd March 2024.
The Eagles are next in action against Everton in the Premier League on Saturday, 15 February.
Palace: Turner (GK), Richards, Lacroix, Guéhi, Muñoz (Kporha, 90), Hughes, Wharton (Lerma, 62), Devenny (Esse, 62), Mitchell (Chilwell, 45), Kamada (Franca, 90+2), Mateta.
Subs: Henderson (GK), Matthews (GK), Clyne
Doncaster: Sharman-Lowe, Maxwell, Sterry (Nixon, 80), Olowu,** Anderson, Bailey, Broadbent (Kelly, 70), Ennis (Senior, 46), Sharp (Ironside, 62), Molyneux, Street (Gibson, 45)
Subs: Crew, Gibson, Lawlor, Nixon, Sbarra, Senior, Westbrooke.
As it Happened