USA international Eddie Lewis set up goals early in the second half for Richard Cresswell and Robbie Blake and a late penalty from substitute Rob Hulse, after Mathias Doumbe had fouled Liam Miller, confirmed the visitors' superiority.
Blackwell, who cut his coaching teeth with Plymouth's youth team under Neil Warnock's management in the mid-1990s, set Lewis on Argyle's right-back Paul Connolly after the interval and turned the game in United's favour.
Argyle were not helped by an injury to absent striker Nick Chadwick and midfielder David Norris' suspension, but Leeds were worthy winners and look a good bet for at least the play-offs.
Leeds' opener came after Argyle's on-loan West Ham centre-back Elliott Ward gave the ball away, allowing Miller to unleash a shot that Plymouth goalkeeper Romain Larrieu turned away for a corner.
Gary Kelly's resulting flag-kick was never cleared and Lewis thumped a ball into the six-yard box that Cresswell easily converted via his head.
Lewis effectively settled the game eight minutes later, crossing for Blake to hammer home a shot that Larrieu could only help into the net.
Cresswell nearly added a third with a diving header from another Lewis cross before Frenchman Doumbe brought down Miller with four minutes remaining, and Hulse grabbed the ball and thumped the spot-kick high past Larrieu.
With Argyle loanees Jason Jarrett and Matt Derbyshire returning to parent clubs Norwich and Blackburn before the weekend, and Ward unable to play in Saturday's FA Cup tie at Wolves, Argyle manager Tony Pulis could be a busy man while the January transfer window remains open.