Price's successful strike two minutes before the interval was just reward for Rovers' total first-half domination.
Coppinger's lobbed shot from 35 yards with 13 minutes to go sealed the win, and Green's sweet volley at the death completed the 3-0 rout, although the travelling side could have netted a hatful more.
After 11 minutes marauding left-back Gareth Roberts hit a 35-yard shot that Millwall keeper Rhys Evans could only parry.
Four minutes later Green rolled a pass to Price with his back to goal in the area. The forward swivelled before blazing his shot over the crossbar.
And still the pressure did not relent for the home team. On 19 minutes Coppinger came even closer to scoring, but his shot could only find the post, much to Evans' relief.
The former Chelsea trainee was forced to limp off ten minutes before half-time, however, after a collision with onrushing Rovers striker Mark McCammon. Preston Edwards came on to replace Evans, but his first job was to pick the ball out of his net.
Price, who looked busy and sharp as the main focus of the Doncaster attack, scored from eight yards after Millwall failed to clear yet another away team corner.
Robert, careering in at the far post, had his shot terrifically blocked, but after the ball ping-ponged in the Millwall area, Price stroked home his fifth goal in the league past the helpless Edwards.
A minute later and forward Gary Alexander squandered Millwall's only decent chance of the game. But, unmarked, he could only head wide from Lewis Grabban's cross.
Coppinger, who impressed with his technical ability, ensured the win with his improvised effort in the 77th minute.
And Green put the icing on the cake for Rovers, who are now unbeaten in 12 games on their travels, with seconds of the game remaining.
Dreams of reaching the second tier for the first time in 50 years are starting to look a reality for Sean O'Driscoll's team.