Goals from Jones and Cotterill in the space of four first-half minutes set Doncaster on their way to their seventh away win of the season.
David Symington pulled one back for Carlisle with a screamer of a free-kick after the break, only for Tommy Spurr to pounce for Rovers' third and seal the victory and extend their unbeaten run on the road to eight games.
It all began going wrong for Carlisle in the 14th minute when Rovers' centre-half Jones came steaming in on to Cotterill's corner to thump a magnificent 12-yard header which gave keeper Adam Collin no chance of saving.
Ian Hume hit the post with a low effort from just inside the area and in the 18th minute Rovers doubled their lead with another spectacular strike, this time from Cotterill who received the ball from Billy Paynter and curled a shot out of the reach of Collin into the top corner of the net.
Symington brought Carlisle back into it in the 66th minute with a superb free-kick from 28 yards which left Gary Woods helpless as it flew and dipped past the Rovers' keeper into the back of the net.
Just as Carlisle were having their best spell of the game Spurr restored Rovers' two-goal advantage in the 77th minute, glancing a header just inside the right hand post from Cotterill's free-kick.