The first 25 minutes was a dire affair in truth but Elliot Lee awoke the game from its slumber with a fantastic volley from inside the box to put the visitors in front. Harry Clifton was then denied after a good, free-flowing counter resulted in his driving shot being parried by Plymouth goalkeeper Luca Ashby-Hammond.
Just as it looked as though Rovers' lead would last until half-time, the hosts drew level through Bim Pepple. Wes Harding had acres of space to pick out his cross which Caleb Watts nodded on for Pepple to prod home.
The hosts then had a glorious chance to go in front just after the break when Owen Bailey's outstretched arm blocked a shot and conceded a penalty. But Zander Clark was the hero as he dived down to his right to keep out a relatively tame Ronan Curtis spot-kick.
The Scotland international, however, was helpless to prevent Argyle going 2-1 up as Herbie Kane's free-kick sailed straight through on its way into the net with no touches from anyone inside the box. Grant McCann rolled the dice with 10 minutes to go as he made four substitutions all at once but the visitors couldn't muster a leveller as they made the long jaunt back to South Yorkshire without anything to show for it.
Here's how we rated the Rovers players in Devon:
9. Robbie Gotts 6
Whistled a shot just wide in the opening exchanges. Took a few knocks from industrial challenges but kept his composure. Photo: Howard Roe/AHPIX LTD
10. Elliot Lee 7
Showed glimpses and had an early shot charged down in the box. Then produced a moment of magic as he unleashed a fierce, dipping volley that flew in to the net for the opener. Was pretty quiet for the rest of the game, mind. Photo: Jonathan Gawthorpe
11. Brandon Hanlan 6
A proper battering ram for Rovers, tasked with holding the ball up and roughing up the Argyle defenders although that came at a personal cost as he failed to register a single shot all game. Photo: Jonathan Gawthorpe
12. Ben Close 5
Saw a shot charged down as Rovers chased an equaliser. Photo: Howard Roe/AHPIX LTD