The Pilgrims, who came into the game on the back of a 1-0 win at Middlesbrough seven days earlier, netted a goal in each half, from Alan Judge and Rory Fallon, either side of Dean Shiels' strike.
Doncaster have not won away from home since April and went behind midway through the first half when Republic of Ireland Under-21 international captain Judge seized on some defensive uncertainty to convert Alan Gow's low left-wing cross.
The lead lasted just three minutes before Shiels grabbed his third goal in four games, firing home from a tight angle after his first effort had been blocked by Fallon.
Doncaster did themselves no favours when captain Martin Woods was dismissed five minutes after the interval for two yellow cards.
He can have no argument about either, going into referee Paul Taylor's notebook first, a minute before half-time, after chopping down Judge.
Five minutes after the break, he committed a similar offence against Iceland international defender Kari Arnason and Taylor showed him a second yellow.
However, it took a while for Woods to leave the field as Taylor was initially unaware he had shown the same player the yellow twice.
The confusion arose because Woods had been wearing a numberless shirt when he received his first caution, the result of having to swap tops because of a bloody nose in the first half.
Argyle capitalised fully when Fallon swooped to fire home a loose ball after Doncaster goalkeeper Neil Sullivan had thwarted Pilgrims' leading scorer Jamie Mackie.
The home side missed a good chance to avoid a nervous final few minutes when Gary Sawyer headed wide after being well set up by Fallon.
However, they hung on in increasingly hard rain to register a win that puts them level on 15 points with their visitors.