There was a big turning point midway through the first half at Home Park.
Joe Morrell went through on goal against high-flying Plymouth, but was forced wide and unable to finish.
The hosts then went straight up the other end of the pitch and Sam Cosgrove fired them into the lead after Mickel Miller’s initial effort had been saved.
Finn Azaz strengthened their advantage after the interval, but Reeco Hackett came off the bench to reduce the deficit and set up a tense finale.
Ryan Hardie wrapped things up for Argyle on the break in stoppage-time and left John Mousinho wondering what might have been.
The Blues boss said: “I actually thought we were the better side overall in the first 45 minutes, but without creating a huge amount.
“We were unlucky to come in behind at the break because we had a great opportunity when Joe Morrell broke through just before they scored.
“Against sides like this, if you don’t take advantage of those opportunities, then you can suddenly find yourselves 1-0 down.
"We were perhaps unfortunate not to get another goal, but we can’t wait until we find ourselves in that position to turn the screw."
“The message at half-time was very positive, but Plymouth were then on top for the next 20 or so minutes and it took going further behind for us to get back in the game.
“We were perhaps unfortunate not to get another goal, but we can’t wait until we find ourselves in that position to turn the screw.
“I thought it was probably a deserved victory for Plymouth in the end, although there were still some positives in there for us.
“Number one is that we didn’t go under and we saw some good performances in there, among others that weren’t so good.
“The substitutes also made a real impact for us, in particular the three who came on earlier. Paddy Lane and Dane Scarlett looked dangerous and Reeco got the goal.”
There was a surprise inclusion when the teams were announced, as Josh Oluwayemi replaced Matt Macey between the sticks.
Mousinho explained: “Matt didn’t travel with us because he was ill, but thankfully we’ve got an able deputy and I thought Josh performed really well.
“He made some excellent saves that kept us in the game, while I felt he was unlucky on a couple of occasions.
“It wasn’t a particularly pleasant one for Matt, so we’ll check in and see how he has ahead of Tuesday.”