Scotland used his power and guile to break the deadlock after taking a superb return pass from playmaker Darren Pratley in his stride before unleashing an unstoppable left-footed drive past home goalkeeper Graham Stack.
It was no more than the hard working Trinidad & Tobago striker deserved, a point acknowledged by proud manager Martinez after the Championship clash.
The Swansea boss said: "It was not just Jason's goal but his overall performance that pleased me. It was the same with the team, it was more important that the performance was there - and it was again.
"I knew that Plymouth would put us under pressure and when they did we were strong enough to stand up to it.
"I would have loved to have scored more goals but it would be wrong of me to be critical of the side after a performance like that.
"Finishing is something that we can work on but I am delighted for Jason that he has got his touch back and his first goal in the Championship. He worked really hard for it."
Martinez brushed aside Plymouth's claims and disallowed an effort from Marcel Seip in the second half while Sturrock was too disappointed to talk about the incident.
He said: "I came to the game with a spring in my step after the way we had trained and felt that we could do something, our shape looked good and I was really looking forward to the game.
"Now though I am flummoxed and I can only apologise to the fans.
"We looked disjointed and we lacked confidence and belief on the ball.
"I don't think Swansea put us under any undue pressure when we had the ball but at least we could have taken more than one touch ... we didn't and we paid the price.
"At the end of the day I ask them to play accurate balls into the strikers and I didn't see any.
"There is a lot of work that needs doing with this squad, I have said it before and I will say it again: it's going to take time, as today proves."
Stack was forced to tip a rising drive from Pratley over his bar in the first minute and in a game of few opportunities the Swans had the best of a dour first half, brought to life by Scotland's incessant chasing - and his goal.
Plymouth's best first-half chance fell to their former Swansea striker Rory Fallon, who flashed a shot wide after 29 minutes.
Stack was tested by Ferrie Bodde but it was not until the closing minutes that Plymouth substitute Jamie Mackie forced a diving save from Swansea goalkeeper Dorus de Vries.
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