Battling Rovers had to settle for a point in an entertaining match at Fratton Park, with only a great late save from home keeper Craig MacGillivray denying Alfie May a late winner.
Mallik Wilks' first-half strike had put Rovers into the lead, but the home side drew level through Omar Bogle in the second period.
Rovers pushed for the winner, with the home keeper in inspired form to tip efforts from John Marquis and May behind.
Rovers' next home game sees them take on Peterborough United on Saturday February 9. Ensure your place at that game by going to tickets.clubdoncaster.co.uk.