Sinclair, who is not 18 until Sunday week, ran three-quarters of the length of the pitch and left two opposition defenders standing three minutes after half-time before curling an exquisite shot past goalkeeper Gabor Kiraly.
The goal was reminiscent of his debut effort against Barnet in the FA Cup and was the fourth he has scored since joining Argyle on loan from Chelsea at the end of the January transfer window.
Sinclair was in his own half when Argyle goalkeeper Luke McCormick cut out a dangerous Palace attack.
McCormick lobbed the ball to Sinclair, who got into his stride and easily brushed off Palace captain Carl Fletcher's challenge.
Danny Butterfield held him up briefly but Sinclair cut inside, took aim and scored a goal that had even his team-mates shaking their heads in disbelief.
The goal ended a miserable week for Argyle manager Ian Holloway, who had seen his side go out of the FA Cup at the quarter-final stage six days earlier and then watched as they were hammered 4-2 at home by Barnsley in midweek.
For Palace, who came to Home Park after four wins and a draw in their last five games, defeat spells the end of any lingering promotion hopes.
McCormick had made a fantastic save to keep the Pilgrims in the game after Tom Soares had played in Ben Watson and defender Leon Cort screwed a golden chance wide.
After Sinclair's goal, Palace sent on striker Dougie Freedman, Shefki Kuqi and Lewis Grabban to end the game with four forwards and Kuqi immediately reached a left-wing Watson corner and headed goalwards only to be thwarted by an acrobatic finger-tip save from McCormick.
Sinclair called Kiraly into the action again with a rising shot after being played through by Barry Hayles, but it was left to his fantastic strike to settle the issue.