Danny Butterfield got the winner as 10-man Palace overcame Gillingham for a sixth win in seven games.
Palace had Mark Hudson sent-off for a foul on Mamady Sidibe to gift the visitors a penalty but they failed to take advantage.
Nicky Southall saw his first penalty palmed onto the woodwork by keeper Cedric Berthelin and hit the crossbar with his re-taken spot-kick.
Butterfield compounded Gillingham's misery when he lashed home his goal.
Hirschfield, on loan from Tottenham, continually thwarted the Eagles but could do little about the goal.
The first clear-cut chance came after 13 minutes to Palace striker Andrew Johnson but his shot was parried to safety by Hirschfeld.
Neil Shipperley had a shot blocked by Barry Ashby after 27 minutes, and Hirschfeld had to be lively again to prevent Julian Gray from opening the scoring with a header.
Cedric Berthelin also had to be alert in the home goal to keep out a fierce 25-yard Rod Wallace strike.
Hirschfeld denied Johnson straight after the break before the turning point in the match.
Hudson was adjudged to have committed a professional foul on Sidibe and was sent off.
Southall twice missed and Butterfield scored soon afterwards when Gillingham only half-cleared.
Crystal Palace: Berthelin, Butterfield, Popovic, Hudson, Granville, Routledge, Hughes, Derry, Gray, Johnson, Shipperley. Subs: Freedman, Black, Borrowdale, Leigertwood, Soares.
Gillingham: Hirschfeld, James, Ashby, Leon Johnson, Rose, Hessenthaler, Smith, Southall, Wallace, Sidibe, Agyemang. Subs: Crofts, Jarvis, Spiller, Pouton, Beckwith.
Referee: P Prosser (Gloucestershire).