The Eagles opened the scoring through Richard Newlove after just nine minutes of play, but the home side were quick to react with a well-worked try finished by debutant Dean Gorton.
Dale Holdstock touched down from close range to give the visitors the advantage at the half-time interval, and in the second half Newlove grabbed his second to make the score 16-4 to Sheffield.
Doncaster had the final say with a try from James Endersby, but that was not enough to prevent a loss in their first game at the new stadium.
"Sure, we would have liked to have won because there was a good crowd and we got a lot of support from the Doncaster public,” said Lakers boss Keiran Dempsey.
“But providing we do our stuff when the season starts in February, hopefully most of them will be back again. Despite the result, I was happy with some of the things that we did and there were some good performances