Grant McCann put Posh ahead in the first half but goals from Brian Stock and Kyle Bennett made it seven points from three matches under Saunders.
After beating Crystal Palace in his first game in charge last Saturday, Saunders named an unchanged team against Hull in midweek. He made one change from that 1-1 draw on Tuesday night as Billy Sharp replaced James Hayter in attack.
New signing Pacsal Chimbonda was left out of the squad as the French defender is short of match fitness.
Peterborough were unchanged from the side that snatched an injury-time victory at Portsmouth in midweek.
Posh flew out of the blocks with Craig Alcock, Emile Sinclair and George Boyd all shooting narrowly wide inside the opening three minutes.
Alcock threatened again from long range in the eighth minute but, once again, his effort went wide.
It was no surprise when Ferguson's side took the lead. McCann beat Neil Sullivan with an unstoppable shot from just out side the area in the 19th minute.
Posh continued to push forward after the goal and Alcock fired wide for a third time.
Rovers goalkeeper Neil Sullivan then had to tip a fiercely-struck free-kick from McCann round the post just before the half-hour mark.
Boyd missed the target from 12 yards before Sullivan produced another fine save to tip Sinclair's shot past the post.
It was much the same story at the start of the second half. Lee Frecklington shot over and then had a goalbound effort block by Shelton Martis before McCann sent an effort wide.
It was against the run of play when Doncaster equalised in the 55th minute. Rovers' first meaningful effort on goal ended up in the back of the net when Brian Stock unleashed an unstoppable shot from 25 yards that flew into the top left-hand corner.
Saunders' side could have been in front immediately afterwards as Jon Parkin hit the crossbar with a shot from the edge of the area.
Doncaster were suddenly rejuvenated and Simon Gillett was the next to go close.
They took the lead in the 67th minute when Bennett converted John Oster's left-wing cross from inside the six-yard box.
Peterborough almost equalised straight away but Sinclair's shot from the left side of the box struck the post.
Sinclair's strike partner Paul Taylor then struck the woodwork from a similar position after 74 minutes.
Posh kept pushing for an equaliser but it was not forthcoming as substitute Ryan Tunnicliffe and Boyd were both denied by Sullivan late on.