Shiels broke the deadlock four minutes after the interval with a curling finish after a neat move and Roberts put the game to bed when he forced home a corner in the final 10 minutes.
Watford only had a brief spell of pressure throughout the 90 minutes, but they reduced the arrears in stoppage time when Heidar Helguson converted a penalty.
The win sees Rovers climb above Watford in the table and harbour realistic hopes of a play-off push in the second half of the season, while Watford were left to contemplate five league games without a win.
This was Doncaster's first game since Boxing Day and they were keen to ensure any cobwebs were blown away as they started the game quickly, creating several chances in the opening 10 minutes.
James Coppinger fired in a shot that deflected off Billy Sharp's knee and was well saved by Scott Loach, before Shiels dragged his shot wide from a good position.
Loach then produced a fine stretching save to deny Shiels and keep the scores level and again he was called into action to turn over Coppinger's cross-shot.
After all their first-half pressure and opportunities, Rovers will have been disappointed to go into the interval level.
But within four minutes of the restart, they finally took the lead their play had deserved.
A fine passing move culminated in Shiels passing the ball to Coppinger and the midfielder delightfully back-heeled the ball back into the path of Shiels, who curled home past Loach and into the bottom corner.
Watford tried to up the ante and Henri Lansbury brought Neil Sullivan into action for the first time in the game when the veteran stopper had to tip over a curling effort. Helguson could not connect properly with a header from the resulting corner.
The Hornets were cranking up the pressure and Sullivan produced a fine save to deny substitute Will Hoskins by getting down well at the near post.
Whilst Watford were searching for a leveller, Doncaster's quick and incisive passing made them dangerous on the break and the Hornets were indebted to Loach for keeping them in the game.
The impressive Shiels broke quickly and got a shot away, which was superbly saved by the England Under-21 stopper and he again denied Sharps by grasping his snap-shot.
But Rovers put the game to bed soon after when they forced a corner, where Roberts was allowed to slam home with seven minutes remaining.
Watford did ensure that the hosts would have a nervy couple of minutes when Helguson dinked home from the penalty spot after Sam Hird had fouled Hoskins.