Coppinger crowned his impressive performance by sealing the win with his fourth goal of the season midway through the first half .
Barnsley suffered from a dismal first-half display but might have snatched a point with a late burst that saw them go close.
In a dreary first half Barnsley's lone striker Andy Gray produced a rare scoring chance when he headed a Ryan Shotton long throw goalwards but Doncaster's veteran keeper Neil Sullivan collected easily.
It was Rovers who made the breakthrough after 35 minutes with a typically patient move after a corner.
Barnsley were caught out ball watching and Coppinger took full advantage with space and time to drive his angled shot out of Luke Steele's reach.
Just after the restart, Billy Sharp worked his way into a good position and collected a short pass from James Hayter but fired wide.
At the other end, Franca Anderson Silva cut in from the right and drilled a low shot out of Sullivan's reach but dragged it wide before Adam Hammill picked out a long-range effort that Sullivan held easily.
Jay Emmanuel-Thomas aimed a dangerous cross to the near post for Sharp but the striker, who is on loan from Sheffield United, messed up his header and it was wide.
Coppinger caused a heart-stopping moment for the home side when he cut in again from the right but Steele hung onto the resulting shot.
Jacob Butterfield arrived as a sub for Barnsley nine minutes into the second half and immediately had an impact improving the home side's midfield
Emmanuel-Thomas, on loan from Arsenal, might have added a second for Rovers when he skipped into the area and rifled a low shot but Darren Moore cleared.
Hugo Roberto Colace came close at the other end but his stinging shot was well saved by Sullivan.