Rovers controlled the majority of the first half and went in at half time ahead thanks to a brilliant finish from Beestin.
However, Darren Ferguson's side failed to build on the lead and always looked susceptible to conceding as Plymouth continued to press.
Ryan Edwards volleyed Argyle level but there was drama right at the death when James Coppinger appeared to be denied a certain penalty after going down under the challenge of Sonny Bradley.
Furious Ferguson had to be restrained from referee Andy Haines following the final whistle.
Rovers made a bright start and went close to taking the lead after 11 minutes when Tommy Rowe curled an effort just wide.
The visitors grew into a closely fought contest and Mathieu Baudry had to deflect an acrobatic attempt from Ryan Taylor wide before Ruben Lameiras wastefully sliced a shot off target from inside the box.
Sandwiched between those chances came the best opening of the game when John Marquis intercepted a pass on half-way, ran clear but his telegraphed shot was kept out by former Rovers loan goalkeeper Remi Matthews.
It was the sort of chance that a game can hinge on.
But, to Marquis's relief, Doncaster did break the deadlock on 37 minutes and the striker played his part in the build-up. He held it up down the left, Jordan Houghton found Tommy Rowe who played in Beestin and the youngster finished with aplomb.
Plymouth pushed for an equaliser following the re-start and in quick succession Bradley saw his header cleared off the line by Matty Blair, Antoni Sarcevic headed another chance over and then Taylor fired just wide.
Darren Ferguson responded by switching to three at the back and bringing on new signing Ben Whiteman and Alfie May.
But it was to no avail as the visitors found the equaliser on 75 minutes and for a third game running Rovers conceded from a set piece. David Fox sent a free kick over from the left and centre back Ryan Edwards, in too much space at the far post, volleyed home.
Plymouth continued to look the more likely to grab a winner and Ian Lawlor survived a big scare when he dropped a cross from the left and Sarcevic failed to scramble it home from close range - only to redeem himself minutes later with a vital save to keep out Sarcevic.
Rovers thought they had a case for a blatant penalty at the death when Coppinger appeared to be brought down, while there was still time for Sarcevic to slice another good chance wide at the other end.
Rovers: Lawlor, Blair, Baudry, Butler, Mason, Houghton, Kongolo (Whiteman 65), Rowe, Coppinger, Beestin (May 65), Marquis. Subs not used: Marosi, Alcock, Wright, Garratt, Ben Khemis, Mandeville.
Plymouth: Matthews, Threlkeld, Edwards, Bradley, Sawyer, Fox, Ness, Sarcevic, Carey, Lameiras (Ainsworth 71), Taylor. Subs not used: Cooper, Miller, Songo'o, Jervis, Grant, Wylde.
Referee: Andy Haines (Tyne and Wear)
Attendance: 7,494 (631)