Rovers midfielder Oster, who joined Doncaster on a free transfer from Palace in August 2009, clinched the South Yorkshire club's first win in 20 matches and lit up an uneventful encounter with a stunning 30-yard shot in the 65th minute.
Rovers were in disarray 24 hours earlier when previous manager Sean O'Driscoll was told he and assistant Richard O'Kelly had been placed on gardening leave via a text message, two days after club chairman John Ryan had publicly backed the Championship's longest-serving manager.
But Doncaster were lying bottom of the table with just one point from their first seven matches and Saunders needed little persuasion to leave his post as Wrexham manager once Ryan and his board decided a change was needed.
Saunders made three changes for his first game in charge. Striker Jon Parkin made his debut after signing on loan this week from Cardiff, midfielder Brian Stock started his first game of the season and centre-half Richard Naylor was also recalled.
Billy Sharp, who damaged ankle ligaments on the opening day of the season, was a surprise inclusion on the substitutes' bench.
Goalkeeper Julian Speroni, Peter Ramage, Aleksander Tunchev, Darren Ambrose, Mile Jedinak, David Wright and Sean Scannell all returned for Palace after sitting out the midweek Carling Cup win over Middlesbrough.
Strikers Scannell and Murray both threatened to make an early breakthrough for the visitors, but scoring chances were at a premium.
Parkin dragged his shot wide for Rovers when well placed in the penalty area and Ambrose was wide with a curling 20-yard effort at the other end as Palace finished the first half on top.
Murray's was twice denied by Rovers goalkeeper Neil Sullivan either side of the interval, his goalbound shot well held and then a header from Ambrose's corner tipped over at full stretch.
Palace continued to dominate possession and Australia international Jedinak volleyed just over from the edge of the area in the 50th minute.
Saunders made a double substitution seven minutes later with Sharp and Slovakian forward Milan Lalkovic replacing Parkin and winger James Coppinger.
The changes did not appear to have much affect, but eight minutes later Oster took possession in his own half and after bursting into opposition territory he unleashed a stunning strike 30 yards from goal that arrowed into Speroni's bottom left-hand corner.
Doncaster striker James Hayter was off target from the edge of the penalty area as the home side chased a second and Oster went close with another rocket, this time from 20 yards, soon after.
By this time it was all one-way traffic and with Palace offering little in attack, Hayter went close to firing a second in the 86th minute, but his close range shot flew the wrong side of the post.