Rovers have recorded just one win against the Canaries in 10 previous meetings - back in 1935 - but midfielder Coppinger clipped the visitors' wings with a stunning opener in the first half and two more in the second period.
Norwich started the game in seventh place, just three points off leaders QPR, but had only one brief spell around the hour mark when they threatened to get back in the game following Russell Martin's brave header.
But Doncaster were already two-up by then and made sure of their third league win of the season when Coppinger's 86th-minute free-kick from 20 yards flew in via a deflection.
Doncaster, who recalled Mustapha Dumbuya and Mark Wilson to the starting line-up, took the game to Norwich in the opening stages.
John Oster and Coppinger both tested Norwich goalkeeper John Ruddy with stinging long-range shots and Rovers were rewarded for their early pressure in the 14th minute.
Coppinger collected the ball in space 30 yards from goal and this time thumped a rising, right-footed drive into the top corner with Ruddy well beaten.
Norwich, for whom the only change saw Anthony McNamee replace Simon Lappin in midfield, responded in the 17th minute when Chris Martin curled their first effort on goal wide from 25 yards.
But Doncaster continued to dominate and peppered the visitors' goal.
Rovers midfielder Simon Gillett twice tried his luck from outside the penalty area, another screamer from the outstanding Coppinger had Ruddy at full stretch again and two typical strikes from Billy Sharp were also saved by the visitors' overworked goalkeeper.
With just the one goal to show for their efforts at half-time, Doncaster picked up where they left off and doubled their lead five minutes after the restart.
Sharp laid the ball off to George Friend on the edge of the area and when his venomous shot was parried by Ruddy, the ball fell to Coppinger six yards out and the Rovers midfielder swept the ball left-footed into the bottom corner.
Two minutes later Norwich striker Martin forced Neil Sullivan into a fine save with a 25-yard free-kick and then the Rovers goalkeeper held Andrew Crofts' header from McNamee's corner.
But back came Doncaster as Ruddy denied them a match-clinching third goal with another brilliant save, this time from Martin Woods, who drilled in a goalbound left-footer from the edge of the penalty area.
Norwich then lifted themselves and following shots just off target from Chris Martin and McNamee, they reduced the deficit in the 64th minute.
Striker Grant Holt clipped the ball back across the goal from the right and defender Russell Martin flung himself headlong to divert the ball past Sullivan into the bottom corner.
The Canaries sensed at this stage that a point was not beyond them and Wes Hoolahan's volley was well held by Sullivan, but Rovers held firm and Coppinger made sure of the spoils in the 86th minute with a 20-yard free-kick that took a deflection.