The Clarets edged the first half with home keeper Neil Sullivan saving James O'Connor's 25-yard strike and Frank Sinclair and Nathan Dyer going close.
But Leeds, who hit the bar with a Matthew Kilgallon header, went ahead when Michael Duff felled Eddie Lewis and David Healy scored from the spot.
Jon Harley had a goal ruled out for the visitors before Blake settled the game with a delightful 25-yard free-kick.
"It's like a bike race, people go way out in front but it's funny how they
get caught. They'll know that they need to keep looking over their shoulder."
Burnley boss Steve Cotterill:
"I don't want to give our former player Robbie Blake any praise, but I thought he was the difference. I thought he was superb.
"If you've got Blake, David Healy, Eddie Lewis, and Rob Hulse in your team, I don't think you can fail to win.
"I think it's the best front line, the best creators in the league. You can argue maybe Wolves, but when Blakey's like that you can't handle him.
"You better ask the referee about Jon Harley's disallowed free-kick.
"If someone else does it and bends it into the top corner (Blake), they say you're a genius, but if Jon Harley does it, we've got to take it again. Maybe he didn't want to give anything contentious.
"I thought we were better than them. If anyone was a betting man there would have been only one team you'd be putting your money on at half-time."
Leeds: Sullivan, Kelly (Douglas 89), Butler, Kilgallon, Harding, Miller, Derry, Lewis, Healy (Richardson 79), Hulse, Blake (Pugh 90).
Subs Not Used: Bennett, Gregan.
Booked: Miller, Healy.
Goals: Healy 55 pen, Blake 70.
Burnley: Jensen, Duff (Elliott 79), Sinclair, McGreal, Lowe, Harley, James O'Connor, Hyde, Spicer (Karbassiyoon 79), Akinbiyi, Dyer.
Subs Not Used: Garreth O'Connor, Noel-Williams, Grant.
Booked: Sinclair, Jensen, McGreal.
Att: 21,318
Ref: T Bates (Staffordshire).