The visitors had taken the lead in the first half courtesy of Steven Caldwell only for the Pilgrims to equalise through Alan Judge soon after.
It was Burnley who were first to break the deadlock when Caldwell managed to get on the end of Blake's cross near the right post.
Despite Pilgrims gloveman Romain Larrieu's best efforts to stretch his limbs to deny the shot, the Clarets captain's header just evaded him.
The visitors kept the lead for all but a minute as winger Judge slotted home from inside the box to equalise for Argyle. The Blackburn Rovers prodigy, on-loan for the remainder of the season, wriggled past two defenders before striking home from an acute angle.
Argyle had the chance to take the lead close to the interval when Jamie Mackie beat his marker inside the box to cross the ball into the path of the oncoming Ashley Barnes. Unfortunately, the striker was denied three yards out by the foot of defender Clarke Carlisle.
The Greens continued to barrage Burnley's goal throughout the second half only for Blake to seal the win for the Clarets late in the game.
The midfielder was quick to spring a counter-attack on the home side and with, economy of effort, struck the back of the net from close range to reclaim the lead.
The Pilgrims had had several chances in the half to seize the lead, their best effort coming just after the hour-mark from Paul Gallagher's free-kick.
The midfielder, also on-loan from Ewood Park, struck with accuracy from 25 yards out but was denied by Burnley keeper Brian Jensen with his last-second deflection.