Doncaster were reduced to 10 men early in the second half when Martin Woods was shown a second yellow card but they went close with Romain Larrieu making a good save from James Coppinger.
However, with 19 minutes remaining Rory Fallon finished well after Jamie Mackie's shot had been saved to give Argyle back-to-back wins.
Doncaster went into the game still looking for their first away win in the league this season and they started well with Woods shooting over from the edge of the area.
In the 16th minute, Billy Sharp got a shot away from the edge of the box but Argyle goalkeeper Larrieu was equal to the effort and made the save.
The home side gradually began to find their rhythm and visiting goalkeeper Neil Sullivan denied Mackie before Shane Lowry went close with a header from six yards following Gow's corner.
Argyle were growing in confidence and duly took the lead with 26 minutes gone when Gow did well to get away down the left and crossed for Judge who toe-poked the ball home.
However, three minutes later Woods' free-kick was met by Shiels and his first shot was blocked but the former Hibernian man hammered in the rebound to draw Doncaster level.
Doncaster immediately went in search of the lead and Shiels' cross found Sharp but his shot was off target.
With half-time approaching, Judge had a sight of goal but Sam Hird did well to block the shot.
Argyle came flying out of the traps after the break and Judge's corner found Fallon who could only head straight at Sullivan.
In the 50th minute, the visitors suffered a blow when Woods was shown a second yellow card for a foul on Kari Arnason.
However, Rovers went close to going in front when James Coppinger found space inside the box but his shot was superbly tipped wide by Larrieu.
The Pilgrims set about making the numerical advantage count and Mackie's shot was saved by Sullivan.
Doncaster were battling well with John Oster dragging a shot wide from the edge of the box before Sharp also went close.
Despite all their efforts, Rovers were unable to prevent Argyle taking the lead with 71 minutes gone when Mackie's shot was saved by Sullivan but Fallon was on hand to bury the rebound.
Doncaster pressed for an equaliser late on but were unable to find a way through.