Darren Ferguson’s Posh extended their winning streak to five games while ending Argyle’s nine-match unbeaten league run. A slip-up by league leaders Lincoln, who drew 2-2 against Swindon, puts Posh at the top of the table, a point clear with two games in hand over third-placed Hull.
Despite plenty of chances in the first half, Peterborough United couldn't open the scoring until the 46th minute.
Argyle goalkeeper Michael Cooper saved from Sammie Szmodics after 13 minutes but could only watch as the United forward fired just wide from 20 yards a minute later.
And just after the half-hour mark, Szmodics blazed over the crossbar after being teed up by Jonson Clarke-Harris.
Argyle’s best first-half opportunity fell to midfielder Panutche Camara. His chest down and goal-bound angled volley was saved by Christy Pym after 40 minutes.
In-form Szmodics broke the deadlock in the opening minutes of the second half, firing Posh ahead from close range as Argyle’s defence failed to clear Joe Ward’s cross from the right.
The striker was also heavily involved in Posh’s second goal, converted by the league’s top scorer Clarke-Harris after 63 minutes. Szmodics' pass from the centre circle out wide on the right to Ward was crossed into the path of on-running Clarke-Harris, who slotted the ball home to score for the sixth successive game.
Peterborough wrapped up the points when Jack Taylor sent a 25-yard strike into the top corner with six minutes remaining.
Speaking after the game, Ferguson said: "It is another 3-0 win in the second half and I can’t remember that happening in my career to be honest, to do that [score three] three games on the bounce.
"It doesn’t matter that we are top of the league at the moment, although you would never turn that position down.
"We knew this would be a massive week, we have won two games away from home which is where we have struggled, either side of a win at home and we will now get some freshness into the players ahead of Saturday.
"From the moment that Sammie scored, we were dominant.
"The second goal that we scored is as good a goal as I have seen all season. The transition, the timing of the pass, the quality of the passing, the assist and Jonno’s finish, it was an outstanding second goal.
"The third goal capped it off. It was a really good away performance.
"We said beforehand that if we can come to a team like Plymouth, who are good at home, on a Tuesday night and come away with three points, that would be a very notable result. We have done just that.
"We will regroup, it is a case of playing the matches, recovering and then playing the matches.
"We won’t get home till 3am but winning can bring that mentality of freshness, if you get what I mean. We look forward to Saturday now."
Posh play Wigan Athletic at the Weston Homes Stadium on Saturday, February 27, kick-off 3pm.