Raiders trailed 31-3 at half-time after initially taking the lead from a Joe Govett penalty.
The Roundstone Lane side, however, put in a positive second-half showing and tested their hosts, who were relegated from the Championship last season.
Converted tries came from Rob Smith and Finlay Coxon-Smith in the second period, while Doncaster also touched down.
Full report and reaction in this week’s paper.