With the victory, they are now up to the 16th spot in the log after accruing 34 points from 34 encounters.
Hodgson's side are now three points clear of the drop zone, although 18th-placed Southampton do have a game in hand. However, they have a brutal final six matches, facing Palace, Tottenham, Burnley, Manchester United, Manchester City and Liverpool, four of which are away from home. The positive, last week, was what Palace manager Hodgson hailed "the best we've played going forward for a long time".
"We've played really well for so many weeks, but we don't end up getting anything from it. I'm just buzzing that we managed to get the win". Given their subsequent problems - through fitness and form - with various strikers, it must be galling for Palace they allowed Murray to leave for just £5million two-and-a-half years ago.More news: Minnesota woman killed woman, assumed her identity
Brighton will be without midfielder Davy Propper through suspension but winger Anthony Knockaert is back from a ban.
An away win would effectively see Brighton secure a second top-flight season on their biggest rivals' pitch.More news: Pelicans being playoff push in Portland
But with local bragging rights on the line, as well as precious points, Palace boss Hodgson knows the pressure that his players will be under after previously steering West Brom and Fulham to survival.
'It's not a classic type of derby; it's one that means more to both clubs than to people outside it. The events use footballers past and present to help highlight issues about racism in social society.More news: Varun Dhawan's Dan comes from a special place