Top scorer Reuben Reid took his goal tally to 20 with a seventh-minute penalty opener, cancelled out by Max Power’s 34th-minute strike.
Three minutes later Argyle surged ahead again thanks to Tareiq Dennis-Holmes’ 30-yard strike.
Lewi Alessandra extended Plymouth’s lead in the 81st-minute before Kayode Odejayi made it 3-2.
Argyle boss John Sheridan said: “With all the frustration we’ve had all season, we’ve still got a chance of getting out of the division and that would be a great achievement.
“We did what we had to do. It was always going to be a bit cagey with Tranmere fighting for their lives, and I thought they gave us a real good go.
“We get the goal early on as well and that gives us a bit of breathing space, but then they score a great goal.
“I would have obviously liked to see the game out a bit easier once we got to 3-1. I’m making substitutes thinking we’re really comfortable but then they get a goal at the end and we’re on a knife edge.
“Tareiq’s got a great strike on him. In training he can’t half hit a ball and luckily for us he’s hit it sweet.
“It’s a great strike and it enabled us to get the advantage again, after the disappointment of switching off a bit for their goal.
“We had to defend but we got the goals and at 3-1, we had chances to get an even better advantage. In the end we got the result we wanted and the result went our way at Southend.”
Tranmere chairman Mark Palios said: “For all the fans and myself it feels devastating but the reality is that tomorrow the sun will come up.
“We have done a lot of things off the park and that will stand us in good stead for the future.
“I don’t want to look back because I don’t think it helps to criticise. But the reality is that this club has been in a bit of a decline for some time and that was the concern when I came in.
“Today our worst fears have been realised. We always knew the die was cast for the season and we tried to rectify that in the transfer window and that didn’t happen.
“The fans today gave me a humbling experience and it makes me more determined that we get back as quickly as we can.
“What I would say to the fans is thank you – they have made themselves heard away from home and at home the gates have continued at high levels given the results we have had on the pitch.
“There is a question that the players didn’t want it enough but I don’t agree with that. You could see today they went right to the end and they were a credit to the club today.”