Heath made the breakthrough after 27 minutes when he reacted first to Blake's corner to head home.
Blake was on target 18 minutes from time to double Leeds' lead, taking advantage of a deflection off Kevin Nicholls to beat Gabor Kiraly.
Palace pulled a goal back after 83 minutes, powering home Mark Kennedy's free-kick, but Leeds held on to win.
Crystal Palace boss Peter Taylor:
"We've got to start another run. I said before the game that we need to get another 30 points to have a chance of getting into sixth place and that's still the target. "I cannot work out why only four extra minutes were played. I know we might not score in the extra time, but even so.
"There's six substitutions, a couple of goals, there's peole going down left, right and centre having treatment, so for four minutes I just cannot work that out."
Leeds: Ankergren, Richardson, Heath, Rui Marques, Lewis (Armando Sa 64), Blake (Foxe 87), Nicholls, Douglas, Westlake, Moore, Kandol (Cresswell 68).
Subs Not Used: Sullivan, Howson.
Goals: Heath 27, Blake 72.
Crystal Palace: Kiraly, Butterfield (Spence 73), Hudson, Cort, Borrowdale, Ifill (Freedman 60), Lawrence, Fletcher, Kennedy, Scowcroft (Kuqi 60), Morrison.
Subs Not Used: Speroni, Ward.
Booked: Butterfield.
Goals: Cort 83.
Att: 19,228
Ref: C Oliver (Northumberland).
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