Doncaster dominated from start to finish and should have had two or three more goals to show for their superiority.
But the visitors' goal led a charmed life and Doncaster set the pattern in the 14th minute when Jason Price had a powerful header tipped over the bar by visiting keeper Paul Smith after Roberts had set up the chance.
Richie Wellens fired just wide with a low shot from the edge of the box seven minutes later before Brett Ormerod posed the first threat for Forest with a 25-yard snap-shot that finished well off the mark.
Doncaster should have taken the lead in the 26th minute when Wellens and the outstanding Paul Green carved out a chance for Paul Heffernan but the Irish striker fired over the bar.
Smith came to the rescue again for Forest when he tipped over a good effort from Green following a brilliant breakaway attack by the home side.
The one-way traffic continued after the interval but Rovers could not find the target with Price ballooning a shot high and wide in the 56th minute before spurning another chance three minutes later.
Despite having their backs to the wall for most of the game Forest should have scored in the 70th minute but substitute Lewis McGugan missed the best chance of the match when he fired wide from point-blank range after being put clean through by Nathan Tyson.
Rovers were finally rewarded for all their pressure when Roberts drilled a low free-kick through the defensive wall from 20 yards and into the net via the inside of the post.
It was no more than they deserved and Forest had Smith to thank for saving them from a heavier defeat when he kept out a cracking low left-footer from Brian Stock with his fingertips in the 79th minute before denying Heffernan with his legs two minutes from time.