It was the revitalised bottom club's fifth game without defeat and their fourth successive clean sheet at home.
Plymouth had won more than they had lost on their travels this season but were too defensive-minded from the start and could have no complaints about the result.
Home keeper Neil Sullivan only had one save to make throughout the match - but what a save it was.
On-loan Blackburn striker Paul Gallagher displayed super control and skill to flick the ball over defender Matt Mills in the 62nd minute before unleashing a tremendous shot from close range.
But the veteran home keeper stood up and made an instinctive save to tip the ball over the crossbar.
Doncaster had most of the first-half play, although the game was scrappy at times during the opening minutes.
James O'Connor produced a weak shot which was comfortably saved in the fifth minute, before Martin Woods hit a dipping effort just over the bar 18 minutes later.
Play was confined to midfield for long periods but Doncaster carved out a great chance in the 35th minute through Richie Wellens and James Coppinger, but Gareth Taylor was just unable to make contact as he slid in with the goal at his mercy.
The game badly needed a goal and Stock provided it with a stunning shot which rocketed into the back of the net off the crossbar in the 37th minute.
Plymouth's attempts to fight back were well contained by the home defence in which Mills was a tower of strength and Doncaster held on to climb off the bottom after taking three deserved points.